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- From Categories to Homotopy Theory , pp. 372 - 383Publisher: Cambridge University PressPrint publication year: 2020
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Adámek, Ji˘rí, Rosický, Ji˘rí, Vitale, Enrico Maria, What are sifted colimits? Theory Appl. Categ. 23 (2010), 251–260. (2)Google Scholar
Frank, J. Adams, On the cobar construction, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 409–412. 10.4.1Google Scholar
Frank Adams, J., Stable homotopy and generalised homology, Reprint of the 1974 original. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL (1995), x+373 pp. 2.2Google Scholar
Frank Adams, J., Infinite loop spaces, Annals of Mathematics Studies, 90. Princeton University Press, Princeton, NJ (1978), x+214 pp. 13.1CrossRefGoogle Scholar
Aguiar, Marcelo, Mahajan, Swapneel, Monoidal functors, species and Hopf algebras, With forewords by Kenneth Brown and Stephen Chase and André Joyal. CRM Monograph Series, 29. American Mathematical Society, Providence, RI (2010), lii+784 pp. 9.7.1, 12.4.4CrossRefGoogle Scholar
Baas, Nils A., Ian Dundas, Bjørn, Rognes, John, Two-vector bundles and forms of elliptic cohomology, in: Topology, geometry and quantum field theory, London Mathematical Society Lecture Note Series, 308, Cambridge University Press, Cambridge (2004), 18–45. 9.1.2, 11.7Google Scholar
Balteanu, Cornel, Fiedorowicz, Roland Schwänzl, Zbigniew, Vogt, Rainer M., Iterated monoidal categories, Adv. Math. 176 (2003), no. 2, 277–349. 14.7, 14.7.2Google Scholar
Barr, Michael, Wells, Charles, Toposes, triples and theories, Corrected reprint of the 1985 original, Repr. Theory Appl. Categ. 12 (2005), x+288 pp. 6.2, 6.4, 6.6Google Scholar
Barratt, Michael G., Eccles, Peter J., +-structures: I. A free group functor for stable homotopy theory, Topology 13 (1974), 25–45. 12.3.9, 14.5.3Google Scholar
Barratt, Michael, Priddy, Steward, On the homology of non-connected monoids and their associated groups, Comment. Math. Helv. 47 (1972), 1–14. 13.2.6Google Scholar
Basterra, Maria, Richter, Birgit, (Co-)homology theories for commutative (S-)algebras, in: Structured ring spectra, London Mathematical Society Lecture Note Series 315, Cambridge University Press (2004), 115–131. 15.5Google Scholar
Michael, A. Batanin, The Eckmann–Hilton argument and higher operads, Adv. Math. 217 (2008), no. 1, 334–385. 14.8, 14.8.11Google Scholar
Baues, Hans Joachim, Wirsching, Günther, Cohomology of small categories, J. Pure Appl. Algebra 38 (1985), no. 2–3, 187–211. 16.4Google Scholar
Beck, Jon, On H-spaces and infinite loop spaces, in: Category theory, homology theory and their applications, III (Battelle Institute Conference, Seattle, Washington, 1968, Vol. 3), Springer, Berlin (1969), 139–153. 10.4.1, 10.5.4Google Scholar
Bénabou, Jean, Introduction to bicategories, Reports of the Midwest Category Seminar, Springer, Berlin (1967), 1–77. 9.6, 9.6.1Google Scholar
Berest, Yuri, Ramadoss, Ajay C., Yeung, Wai-Kit, Representation homology of spaces and higher Hochschild homology, preprint arXiv:1703.03505. 14.1Google Scholar
Berger, Clemens, Combinatorial models for real configuration spaces and En-operads, Operads: Proceedings of Renaissance Conferences (Hartford, CT/Luminy, 1995), Contemporary Mathematics, 202. American Mathematical Society, Providence, RI (1997), 37–52. 12.3.9Google Scholar
Berger, Clemens, Double loop spaces, braided monoidal categories and algebraic 3-type of space, Higher homotopy structures in topology and mathematical physics (Poughkeepsie, NY, 1996). Contemporary Mathematics, 227, American Mathematical Society, Providence, RI (1999), 49–66. 14.6Google Scholar
Berger, Clemens, Iterated wreath product of the simplex category and iterated loop spaces, Adv. Math. 213 (2007), 230–270. 14.8, 14.8.1, 14.8.1, 14.8.2, 14.8.20Google Scholar
Bergner, Julia E., Simplicial monoids and Segal categories, Categories in algebra, geometry and mathematical physics, Contemporary Mathematics, 431. American Mathematical Society, Providence, RI (2007), 59–83. 10.14.4Google Scholar
Bergner, Julia E., The homotopy theory of (∞,1)-categories, London Mathematical Society Student Texts, 90. Cambridge University Press, Cambridge (2018), xiv+273 pp. (document), 14.8.3Google Scholar
Bergner, Julia E., A survey of models for (∞,n)-categories, in: Handbook of Homotopy Theory, edited by Haynes Miller, Chapman & Hall/CRC (2020), 263–295. 14.8.3Google Scholar
Bergner, Julia E., Rezk, Charles, Reedy categories and the construction, Math. Z. 274 (2013), no. 1–2, 499–514. 14.8Google Scholar
Bergner, Julia E., Rezk, Charles, Comparison of models for (∞,n)categories, I, Geom. Topol. 17 (2013), no. 4, 2163–2202. 14.8, 14.8.3Google Scholar
Bergner, Julia E., Rezk, Charles, Comparison of models for (∞,n)categories, II, preprint arXiv:1406.4182. 14.8, 14.8.3Google Scholar
Boardman, J. Michael, Vogt, Rainer M., Homotopy-everything H-spaces, Bull. Amer. Math. Soc. 74 (1968), 1117–1122. 12, 12.3.2Google Scholar
Boardman, J. Michael, Rainer M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics, Vol. 347, Springer-Verlag, Berlin and New York (1973), x+257 pp. 10.13, 12, 12.3.2Google Scholar
Borceux, Francis, Handbook of Categorical Algebra 1, Basic Category Theory, Encyclopedia of Mathematics and Its Applications, Cambridge University Press (1994), xvi+345 pp. (document), 1.3, 4, 4.1Google Scholar
Borceux, Francis, Handbook of Categorical Algebra 2, Categories and Structures, Encyclopedia of Mathematics and Its Applications, Cambridge University Press (1994), xviii+443 pp. (document), 6.4, 6.6, 7.3, 9Google Scholar
Aldridge, K. Bousfield, On the homology spectral sequence of a cosimplicial space, Amer. J. Math. 109 (1987), no. 2, 361–394. 10.4.1Google Scholar
Bousfield, Aldridge K., Friedlander, Eric M., Homotopy theory of -spaces, spectra, and bisimplicial sets, Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977), II, pp. 80–130, Lecture Notes in Mathematics, 658, Springer, Berlin (1978). 14.3CrossRefGoogle Scholar
Bousfield, Aldridge K., Kan, Daniel M., Homotopy limits, completions and localizations, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin and New York (1972), v+348 pp. 10.8.6, 10.10, 10.10.4, 11.4, 11.4, 11.4, 11.4.1Google Scholar
Browder, William, Homology operations and loop spaces, Illinois J. Math. 4 1960, 347–357. 12.3.3Google Scholar
Cartan, Henri, Eilenberg, Samuel, Homological algebra, With an appendix by David A. Buchsbaum. Reprint of the 1956 original. Princeton Landmarks in Mathematics. Princeton University Press, Princeton, NJ (1999), xvi+390 pp. 15.2.4Google Scholar
Church, Thomas, Ellenberg, Jordan S., Farb, Benson, FI-modules and stability for representations of symmetric groups, Duke Math. J. 164 (2015), no. 9, 1833–1910. 9.7.1Google Scholar
Peter, V. Z. Cobb, Pn-spaces and n-fold loop spaces, Bull. Amer. Math. Soc. 80 (1974), 910–914. 14.7, 14.8.2Google Scholar
Cohen, Frederick R., Lada, Thomas J., Peter May, J., The homology of iterated loop spaces, Lecture Notes in Mathematics, Vol. 533, Springer-Verlag, Berlin and New York (1976), vii+490 pp. 12.3.3, 12.3.3, 13.4.5Google Scholar
Davis, James F., Kirk, Paul, Lecture notes in algebraic topology, Graduate Studies in Mathematics, 35. American Mathematical Society, Providence, RI (2001), xvi+367 pp. 1.4.6, 13.4Google Scholar
Day, Brian, Construction of Biclosed Categories, PhD Thesis, University of New South Wales (1970), available at www.math.mq.edu.au/∼street/DayPhD.pdf. 9Google Scholar
Day, Brian, On closed categories of functors, 1970 Reports of the Midwest Category Seminar, IV pp. 1–38, Lecture Notes in Mathematics, Vol. 137, Springer, Berlin (1970). 9, 9.8Google Scholar
Djament, Aurélien, Décomposition de Hodge pour l’homologie stable des groupes d’automorphismes des groupes libres, preprint arXiv:1510.03546. 15.3Google Scholar
Dold, Albrecht, Homology of symmetric products and other functors of complexes, Ann. of Math. (2) 68 (1958), 54–80. 10.11, 10.11.2, 10.11Google Scholar
Eduardo, J. Dubuc, Kan extensions in enriched category theory, Lecture Notes in Mathematics, Vol. 145, Springer-Verlag, Berlin and New York (1970), xvi+173 pp. 4, 9Google Scholar
Dugger, Daniel, A primer on homotopy colimits, notes available at pages.uoregon.edu/ddugger 11.4, (4), 11.4.6Google Scholar
Dugger, Daniel, Shipley, Brooke, Topological equivalences for differential graded algebras, Adv. Math. 212 (2007), no. 1, 37–61. 8.1.15Google Scholar
Dundas, Bjørn Ian, Goodwillie, Thomas G., McCarthy, Randy, The local structure of algebraic K-theory, Algebra and Applications, 18. Springer-Verlag London, Ltd., London (2013), xvi+435 pp. (document), 14.3.15Google Scholar
William, G. Dwyer, Strong convergence of the Eilenberg–Moore spectral sequence, Topology 13 (1974), 255–265. 10.4.1Google Scholar
William, G. Dwyer, Hirschhorn, Philip S., Kan, Daniel M., Smith, Jeffrey H., Homotopy limit functors on model categories and homotopical categories, Mathematical Surveys and Monographs, 113. American Mathematical Society, Providence, RI (2004), viii+181 pp. 11.4.7Google Scholar
William, G. Dwyer, Spaliński,´, Jan Homotopy theories and model categories, Handbook of algebraic topology, North-Holland, Amsterdam (1995), 73–126. (document)Google Scholar
Dyer, Eldon, Lashof, Richard K., Homology of iterated loop spaces, Amer. J. Math. 84 (1962), 35–88. 12.3.3Google Scholar
Eckmann, Benno, Hilton, Peter J., Group-like structures in general categories: I. Multiplications and comultiplications, Math. Ann. 145 (1961/1962), 227–255. 8.1.3Google Scholar
Eilenberg, Samuel, Zilber, Joseph A., Semi-simplicial complexes and singular homology, Ann. of Math. (2) 51 (1950), 499–513. 10Google Scholar
Anthony, D. Elmendorf, Mandell, Michael A., Rings, modules, and algebras in infinite loop space theory, Adv. Math. 205 (2006), no. 1, 163–228. 14.4Google Scholar
Fiedorowicz, Zbigniew, The symmetric bar construction, preprint, available at https://people.math.osu.edu/fiedorowicz.1/14.6Google Scholar
Fiedorowicz, Zbigniew, Loday, Jean-Louis, Crossed simplicial groups and their associated homology, Trans. Amer. Math. Soc. 326 (1991), no. 1, 57–87. 14.6, 14.6.1, 15.4.3Google Scholar
Franjou, Vincent, Pirashvili, Teimuraz, On the Mac Lane cohomology for the ring of integers, Topology 37 (1998), no. 1, 109–114. 15.3Google Scholar
Franjou, Vincent, Friedlander, Eric M., Pirashvili, Teimuraz, Schwartz, Lionel, Rational representations, the Steenrod algebra and functor homology, Panoramas et Synthèses, 16. Société Mathématique de France, Paris (2003), xxii+132 pp. 15.2.4, 15.3, 15.6.2, 16.5Google Scholar
Fresse, Benoit, Modules over operads and functors, Lecture Notes in Mathematics, 1967, Springer-Verlag, Berlin (2009), x+308 pp. 12Google Scholar
Gabriel, Peter, Ulmer, Friedrich, Lokal Präsentierbare Kategorien, Lecture Notes in Mathematics, Vol. 221. Springer-Verlag, Berlin and New York (1971), v+200 pp. 5.3Google Scholar
Gabriel, Peter, Zisman, Michel, Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35, Springer-Verlag New York, Inc., New York (1967), x+168 pp. 10, 10.6.9, 11.5, 11.5, 11.5.4, 11.5, 16.5.8Google Scholar
Galvez-Carrillo, Imma, Neumann, Frank, Tonks, Andrew, Thomason cohomology of categories, J. Pure Appl. Algebra 217 (2013), no. 11, 2163–2179. 16.1, 16.4.2Google Scholar
Izrail, M. Gelfand, Kapranov, Mikhail M., Zelevinsky, Andrey V., Discriminants, resultants and multidimensional determinants, Reprint of the 1994 edition. Modern Birkhäuser Classics. Birkhäuser Boston, Inc., Boston, MA (2008), x+523 pp. 12.3.4Google Scholar
Paul, G. Goerss, Hopkins, Michael J., Moduli spaces of commutative ring spectra, Structured ring spectra, London Math. Soc. Lecture Note Ser., 315, Cambridge Univ. Press, Cambridge (2004), 151–200. 10.10.4, 15.5Google Scholar
Paul, G. Goerss, Jardine, John F., Simplicial homotopy theory, Reprint of the 1999 edition. Modern Birkhäuser Classics, Birkhäuser Verlag, Basel (2009), xvi+510 pp. 10, 10.4.1, 10.11, 10.12.12, 11.1, 11.7Google Scholar
Grayson, Daniel, Higher algebraic K-theory. II (after Daniel Quillen), Algebraic K-theory (Proc. Conf., Northwestern University, Evanston, Ill., 1976), Lecture Notes in Mathematics, Vol. 551, Springer, Berlin (1976), 217–240. (document), 13.3, 13.4.6Google Scholar
Groth, Moritz, A short course on ∞-categories, in: Handbook of Homotopy Theory, edited by Haynes Miller, Chapman & Hall/CRC (2020), 549–617. (document), 11.8.2, 11.8.3, 11.8.13, 11.8.3Google Scholar
Grothendieck, Alexander, Revêtements étales et groupe fondamental (SGA 1), Séminaire de géométrie algébrique du Bois Marie 1960–61. Directed by A. Grothendieck. With two papers by M. Raynaud, Updated and annotated reprint of the 1971 original (Lecture Notes in Mathematics, 224, Springer, Berlin. Documents Mathématiques (Paris), 3. Société Mathématique de France, Paris (2003), xviii+327 pp. 9.6.5, 11.6Google Scholar
Hatcher, Allen, Algebraic topology, Cambridge University Press, Cambridge (2002), xii+544 pp. 11.7, 13.1.2, 13.4Google Scholar
Hess, Kathryn, Tonks, Andrew, The loop group and the cobar construction, Proc. Amer. Math. Soc. 138 (2010), no. 5, 1861–1876. 10.4.1Google Scholar
Philip, S. Hirschhorn, Model categories and their localizations, Mathematical Surveys and Monographs, 99. American Mathematical Society, Providence, RI (2003), xvi+457. (document), 11.4.7, 11.4.1Google Scholar
Philip, S. Hirschhorn, Notes on homotopy colimits and homotopy limits, work in progress, available at www-math.mit.edu/∼psh/ notes/hocolim.pdf 11.4.10Google Scholar
Hoffbeck, Eric, Vespa, Christine, Leibniz homology of Lie algebras as functor homology, J. Pure Appl. Algebra 219 (2015), no. 9, 3721–3742. 15.3.3, 15.3.3Google Scholar
Karl, H. Hofmann, Morris, Sidney A., The structure of compact groups. A primer for the student – a handbook for the expert, Third edition, revised and augmented. De Gruyter Studies in Mathematics, 25. De Gruyter, Berlin (2013), xxii+924 pp.1.3Google Scholar
Hovey, Mark, Model categories, Mathematical Surveys and Monographs, 63. American Mathematical Society, Providence, RI (1999), xii+209 pp. (document)Google Scholar
Hovey, Mark, Spectra and symmetric spectra in general model categories, J. Pure Appl. Algebra 165 (2001), no. 1, 63–127. 10.15Google Scholar
Hovey, Mark, Palmieri, John H., Strickland, Neil P., Axiomatic stable homotopy theory, Mem. Amer. Math. Soc. 128 (1997), no. 610, x+114 pp. 8.4.7Google Scholar
Hovey, Mark, Shipley, Brooke, Smith, Jeffrey H., Symmetric spectra, J. Amer. Math. Soc. 13 (2000), no. 1, 149–208. 10.15, 10.15, 10.15Google Scholar
Jibladze, Mamuka, Pirashvili, Teimuraz, Cohomology of algebraic theories, J. Algebra 137 (1991), no. 2, 253–296. 16.5, 16.5.1, 16.5.2, 16.5.3, 16.5.4, 16.5.5Google Scholar
Joyal, André, Disks, duality and -categories, preprint, available on https://ncatlab.org/nlab/files/JoyalThetaCategories.pdf. 10.3, 10.3, 14.8, 14.8.1, 14.8.11, 14.8.1, 14.8.1Google Scholar
Joyal, André, Quasi-categories versus simplicial categories, preprint, available at www.math.uchicago.edu/∼may/IMA/Incoming/Joyal/QvsDJan9(2007).pdf 10.13Google Scholar
Joyal, André, The Theory of Quasi-categories and its Applications, book, available at www.mat.uab.cat/∼kock/crm/hocat/advanced-course/Quadern45-2.pdf. 5.1.2, 10.13, 11.1, 11.8.3, 11.8.11, 11.8.12, 11.8.3Google Scholar
Joyal, André, Quasi-categories and Kan complexes, Special volume celebrating the 70th birthday of Professor Max Kelly. J. Pure Appl. Algebra 175 (2002), no. 1-3, 207–222. 10.13Google Scholar
Joyal, André, Street, Ross, Braided tensor categories, Adv. Math. 102 (1993), no. 1, 20–78. 8.6Google Scholar
Daniel, M. Kan, A combinatorial definition of homotopy groups, Ann. Math. 67 (1958), no. 2, 282–312. 10Google Scholar
Daniel, M. Kan, Thurston, William Paul, Every connected space has the homology of a K(π,1), Topology 15 (1976), no. 3, 253–258. 13.4.7Google Scholar
Mikhail, M. Kapranov, The permutoassociahedron, Mac Lane’s coherence theorem and asymptotic zones for the KZ equation, J. Pure Appl. Algebra 85 (1993), no. 2, 119–142. 12.3.4Google Scholar
Kashiwabara, Takuji, On the homotopy type of configuration complexes. Algebraic topology, (Oaxtepec, 1991), Contemp. Math., 146, Amer. Math. Soc., Providence, RI (1993), 159–170. 12.3.9Google Scholar
Kassel, Christian, Quantum groups, Graduate Texts in Mathematics, 155. Springer-Verlag, New York (1995), xii+531 pp. 8.6, 8.6.9CrossRefGoogle Scholar
Kelly, Gregory Maxwell, On MacLane’s conditions for coherence of natural associativities, commutativities, etc, J. Algebra 1 (1964), 397–402. 8.1Google Scholar
Kelly, Gregory Maxwell, Basic concepts of enriched category theory, London Mathematical Society Lecture Note Series, 64. Cambridge University Press, Cambridge-New York (1982), 245 pp. 8.1.13, 9Google Scholar
Kudo, Tatsuji; Araki, Shôrô, Topology of Hn-spaces and H-squaring operations, Mem. Fac. Sci. Kyūsyū Univ. Ser. A. 10 (1956), 85–120.¯ 12.3.3Google Scholar
Latch, Dana May, Thomason, Robert W., Wilson, W. Stephen, Simplicial sets from categories, Math. Z. 164 (1979), no. 3, 195–214. 11.1.8Google Scholar
Lawson, Tyler, Commutative -rings do not model all commutative ring spectra, Homology, Homotopy Appl. 11 (2009), no. 2, 189–194. 14.3.15Google Scholar
Livernet, Muriel, Richter, Birgit, An interpretation of En-homology as functor homology, Math. Z. 269 (2011), no. 1-2, 193–219. 14.8.2, 15.3, 15.3.3, 15.3.3Google Scholar
Loday, Jean-Louis, La renaissance des opérades, Séminaire Bourbaki volume 1994/95, exposés 790–804, Astérisque no. 237 (1994–1995), Talk no. 792, p. 47–74. 12Google Scholar
Loday, Jean-Louis, Cyclic homology, Appendix E by María O. Ronco, Second edition. Chapter 13 by the author in collaboration with Teimuraz Pirashvili, Grundlehren der Mathematischen Wissenschaften 301, Springer-Verlag, Berlin (1998), xx+513 pp. 15, 15.3, 15.3, 15.3.10Google Scholar
Loday, Jean-Louis, Realization of the Stasheff polytope, Arch. Math. (Basel) 83 (2004), no. 3, 267–278. 12.3.4, 12.3.11, 12.3.4Google Scholar
Loday, Jean-Louis, Bruno Vallette, Algebraic operads, Grundlehren der Mathematischen Wissenschaften 346, Springer, Heidelberg (2012), xxiv+634 pp. 12Google Scholar
Lurie, Jacob, Higher topos theory, Annals of Mathematics Studies, 170. Princeton University Press, Princeton, NJ (2009), xviii+925 pp. (document), 4.6.2, 5.1.2, 9, 10.13, 10.13.5, 11.1.3, 11.8.3, 11.8.11, 11.8.3, 11.8.3, 14.8.3Google Scholar
Lurie, Jacob, Higher Algebra, book draft, available at www.math.harvard.edu/∼lurie/. (document), 5.1.2, 11.6, 11.8.2, 11.8.2, 11.8.3, 12.3.4
Google Scholar
Lydakis, Manos, Smash products and -spaces, Math. Proc. Cambridge Philos. Soc. 126 (1999), no. 2, 311–328. 14.3.15Google Scholar
MacDonald, John, Sobral, Manuela, Aspects of monads, in: Categorical foundations, Encyclopedia Math. Appl., 97, Cambridge Univ. Press, Cambridge (2004), 213–268.Google Scholar
Lane, Saunders Mac, Natural associativity and commutativity, Rice Univ. Studies 49 (1963), no. 4, 28–46. 8.1, 8.1.8Google Scholar
Lane, Saunders Mac, Categories for the working mathematician, Graduate Texts in Mathematics. 5, 2nd ed., Springer (1998), xii+314 pp. (document), 3.1, 4, 4.7, 6.6, 8.1.8, (1), 8.6, 8.6.7Google Scholar
Michael, A. Mandell, May, J. Peter, Schwede, Stefan, Shipley, Brooke, Model categories of diagram spectra. Proc. London Math. Soc. (3) 82 (2001), no. 2, 441–512. 9.8Google Scholar
Markl, Martin, Shnider, Steve, Stasheff, Jim, Operads in algebra, topology and physics, Mathematical Surveys and Monographs, 96, American Mathematical Society, Providence, RI (2002), x+349 pp. 12Google Scholar
Peter May, J., Simplicial objects in algebraic topology, Reprint of the 1967 original. Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL (1992), viii+161 pp. 10, 10.6.4, 10.12.12Google Scholar
Peter May, J., The geometry of iterated loop spaces, Lectures Notes in Mathematics, Vol. 271. Springer-Verlag, Berlin-New York (1972), viii+175 pp. 10.4.1, 10.4.1, 10.5.3, 10.5.4, 12, 12.3.2, 12.3.7Google Scholar
Peter May, J., E∞ spaces, group completions, and permutative categories, New developments in topology (Proc. Sympos. Algebraic Topology, Oxford, 1972), London Math. Soc. Lecture Note Ser., No. 11, Cambridge Univ. Press, London (1974), pp. 61–93. 8.3.6, 13.1.5, 13.1, 13.4.4, 13.4.5Google Scholar
Peter May, J., E∞ ring spaces and E∞ ring spectra, with contributions by Frank Quinn, Nigel Ray, and Jørgen Tornehave, Lecture Notes in Mathematics, Vol. 577. Springer-Verlag, Berlin-New York (1977), 268 pp. 14.4Google Scholar
Peter May, J., The spectra associated to permutative categories, Topology 17 (1978), no. 3, 225–228. 14.4Google Scholar
Peter May, J., A concise course in algebraic topology, Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, (1999), x+243 pp. 8.5Google Scholar
Peter May, J., Thomason, Robert W., The uniqueness of infinite loop space machines, Topology 17 (1978), 205–224. 14.1, 14.1Google Scholar
McCleary, John, A user’s guide to spectral sequences, Second edition. Cambridge Studies in Advanced Mathematics, 58. Cambridge University Press, Cambridge (2001), xvi+561 pp. 10.4.1Google Scholar
Michael, C. McCord, Classifying spaces and infinite symmetric products, Trans. Amer. Math. Soc. 146 (1969), 273–298. 8.5Google Scholar
McDuff, Dusa, On the classifying spaces of discrete monoids, Topology 18 (1979), no. 4, 313–320. 13.4.7Google Scholar
Milnor, John, On the construction FK, notes from 1955, printed in J. Frank Adams, Algebraic Topology – A Student’s Guide, London Mathematical Society Lecture Note Series (4), Cambridge University Press (1972), 118–136. 12.3.9Google Scholar
Milnor, John, The geometric realization of a semi-simplicial complex, Ann. of Math. (2) 65 (1957), 357–362. 10.6, 10.6.4, 10.6Google Scholar
John, C. Moore, Homotopie des complexes monoïdaux, I. Séminaire Henri Cartan, 7 no. 2 (1954-1955), Exp. No. 18, 8 p. 10.11, 10.12.10Google Scholar
Nikolaus, Thomas, Sagave, Steffen, Presentably symmetric monoidal ∞-categories are represented by symmetric monoidal model categories, Algebr. Geom. Topol. 17 (2017), no. 5, 3189–3212. 11.8.3Google Scholar
Oury, David, On the duality between trees and disks, Theory Appl. Categ. 24 (2010), No. 16, 418–450. 10.3Google Scholar
Pedicchio, Maria Cristina, Solimini, Sergio, On a “good” dense class of topological spaces, J. Pure Appl. Algebra 42 (1986), no. 3, 287–295. 8.4.4Google Scholar
Pirashvili, Teimuraz, Hodge decomposition for higher order Hochschild homology, Ann. Sci. École Norm. Sup. (4) 33 (2000), 151–179. 15Google Scholar
Pirashvili, Teimuraz, Dold-Kan type theorem for -groups, Math. Ann. 318 (2000), no. 2, 277–298.Google Scholar
Pirashvili, Teimuraz, On the PROP corresponding to bialgebras, Cah. Topol. Géom. Différ. Catég. 43 (2002), no. 3, 221–239. 14.1.6Google Scholar
Pirashvili, Teimuraz, Richter, Birgit, Robinson-Whitehouse complex and stable homotopy, Topology 39 (2000), no. 3, 525–530. (4), 15, 15.3, 15.3.3, 15.5Google Scholar
Pirashvili, Teimuraz, Richter, Birgit, Hochschild and cyclic homology via functor homology, K-Theory 25 (2002), no. 1, 39–49. 15.3, 15.3.3, 15.3.9, 15.4.1, 15.4.3, 15.4Google Scholar
Daniel, G. Quillen, Homotopical algebra, Lecture Notes in Mathematics, No. 43 Springer-Verlag, Berlin-New York (1967), iv+156 pp. (document), 10Google Scholar
Daniel, G. Quillen, Rational homotopy theory, Ann. of Math. (2) 90 (1969), 205–295. 10.4.1Google Scholar
Daniel, G. Quillen, On the (co-)homology of commutative rings, Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol. XVII, New York, 1968), Amer. Math. Soc., Providence, R.I. (1970), pp. 65–87. 5.1Google Scholar
Daniel, G. Quillen, Higher algebraic K-theory: I, in: Algebraic Ktheory, I: Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), Lecture Notes in Math., Vol. 341, Springer, Berlin (1973), 85–147. (document), 10.8, 11.2, 11.5, 11.5, 11.5.6, 11.6, 11.7.2, 11.7, 11.7.7, 11.7.8, 16.2, 16.2.3Google Scholar
Daniel, G. Quillen, On the group completion of a simplicial monoid, Appendix Q in: Eric Friedlander, Barry Mazur, Filtrations on the homology of algebraic varieties, Mem. Amer. Math. Soc. 110 (1994), no. 529, x+110 pp. 13.4.2Google Scholar
Reedy, Christopher Leonard, Homotopy theory of model categories, unpublished preprint, available at www-math.mit.edu/~psh/ 10.8.6Google Scholar
Reutenauer, Christophe, Free Lie algebras, London Mathematical Society Monographs. New Series, 7. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York (1993), xviii+269 pp. 2.4.2Google Scholar
Rezk, Charles, A Cartesian presentation of weak n-categories, Geom. Topol. 14 (2010), no. 1, 521–571. See also: Charles Rezk, Correction to ‘A Cartesian presentation of weak n-categories’, Geom. Topol. 14 (2010), no. 4, 2301–2304. 14.8, 14.8.3Google Scholar
Rezk, Charles, When are homotopy colimits compatible with homotopy pullbacks, note available at www.faculty.math.illinois.edu/∼rezk/i-hate-the-pi-star-kan-condition.pdf 11.4.10Google Scholar
Richter, Birgit, Symmetry properties of the Dold-Kan correspondence, Math. Proc. Cambridge Philos. Soc. 134 (2003), no. 1, 95–102. 9.3, 12.4, 12.4.2, 12.4.3, 12.4Google Scholar
Richter, Birgit, Robinson, Alan, Gamma homology of group algebras and of polynomial algebras, Homotopy theory: relations with algebraic geometry, group cohomology, and algebraic K-theory, Contemp. Math., 346, Amer. Math. Soc., Providence, RI (2004), 453–461. 15.5, 15.5.3Google Scholar
Richter, Birgit, Sagave, Steffen, A strictly commutative model for the cochain algebra of a space, preprint, arXiv:1801.01060. 11.4.7Google Scholar
Richter, Birgit, Shipley, Brooke, An algebraic model for commutative HZ-algebras, Algebraic and Geometric Topology 17 (2017), 2013–2038. 9.8.9, 10.15.3Google Scholar
Riehl, Emily, Categorical Homotopy Theory, New Mathematical Monographs, 24. Cambridge University Press, Cambridge (2014), xviii+352 pp. 4, 8.5, 9, 11.4.7Google Scholar
Riehl, Emily, Category theory in context, Aurora Dover Modern Math Originals, Mineola, NY: Dover Publications (2016), xvii, 234 p. (document), 6.3Google Scholar
Robinson, Alan, Gamma homology, Lie representations and E∞ multiplications, Invent. Math. 152 (2003), no. 2, 331–348. 15.5Google Scholar
Robinson, Alan, Whitehouse, Sarah, Operads and -homology of commutative rings, Math. Proc. Cambridge Philos. Soc. 132 (2002), 197–234. (4), 15.5Google Scholar
González, Beatriz Rodríguez, Simplicial descent categories, J. Pure Appl. Algebra 216 (2012), no. 4, 775–788. 11.4.7Google Scholar
González, Beatriz Rodríguez, Realizable homotopy colimits, Theory Appl. Categ. 29 (2014), No. 22, 609–634. 11.4.7Google Scholar
Rosický, Jiˇrí, On homotopy varieties, Adv. Math. 214 (2007), no. 2, 525–550. 11.4.1, 11.4.9Google Scholar
Sagave, Steffen, Schlichtkrull, Christian, Diagram spaces and symmetric spectra, Adv. Math. 231 (2012), no. 3-4, 2116–2193. 9.7.1, 9.8.9, 13.3.8, 14.5Google Scholar
Schlichtkrull, Christian, The homotopy infinite symmetric product represents stable homotopy, Algebr. Geom. Topol. 7 (2007), 1963–1977. 14.5.3Google Scholar
Schlichtkrull, Christian, Thom spectra that are symmetric spectra, Doc. Math. 14 (2009), 699–748. 14.5Google Scholar
Schlichtkrull, Christian, Solberg, Mirjam, Braided injections and double loop spaces, Trans. Amer. Math. Soc. 368 (2016), no. 10, 7305–7338. 8.6.8, 14.6, 14.6, 14.6.3, 14.6, 14.6.6Google Scholar
Schubert, Horst, Kategorien. I, II, Heidelberger Taschenbücher, Bände 65, 66, Springer (1970). (document), 1.4.5, 2.3.3Google Scholar
Schwede, Stefan, Stable homotopical algebra and -spaces, Math. Proc. Cambridge Philos. Soc. 126 (1999), no. 2, 329–356. 14.3.15Google Scholar
Schwede, Stefan, An untitled book project about symmtric spectra, file available at www.math.uni-bonn.de/people/schwede/SymSpec-v3.pdf 10.15Google Scholar
Segal, Graeme, Classifying spaces and spectral sequences, Inst. Hautes Études Sci. Publ. Math. No. 34 (1968), 105–112.Google Scholar
Segal, Graeme, Configuration-spaces and iterated loop-spaces, Invent. Math. 21 (1973), 213–221. 13.4.5Google Scholar
Segal, Graeme, Categories and cohomology theories, Topology 13 (1974), 293–312. 9.7.1, 10.6.10, 10.9.1, 10.9.2, 10.9.4, 10.9, 11.2, 14.2.3, 14.2, 14.3, (2), 14.3.13, 14.4Google Scholar
Brooke, E. Shipley, Convergence of the homology spectral sequence of a cosimplicial space, Amer. J. Math. 118 (1996), no. 1, 179–207. 10.4.1Google Scholar
Słominska, Jolanta,´ Decompositions of the category of noncommutative sets and Hochschild and cyclic homology, Cent. Eur. J. Math. 1 (2003), no. 3, 327–331. 15.3.10Google Scholar
Smith, Larry, Lectures on the Eilenberg-Moore spectral sequence, Lecture Notes in Mathematics, Vol. 134 Springer-Verlag, Berlin-New York (1970), vii+142 pp. 10.4.1Google Scholar
Smith, Jeffrey Henderson, Simplicial group models for nSn X, Israel J. Math. 66 (1989), no. 1-3, 330–350. 12.3.9Google Scholar
Srinivas, Vasudevan, Algebraic K-theory, Second edition. Progress in Mathematics, 90. Birkhäuser Boston, Inc., Boston, MA, 1996. xviii+341 pp. 11.7Google Scholar
Richard, P. Stanley, Enumerative combinatorics. Vol. 2, Cambridge Studies in Advanced Mathematics, 62. Cambridge University Press, Cambridge (1999), xii+581 pp. 12.3.4Google Scholar
James, D. Stasheff, Homotopy associativity of H-spaces. I, II, Trans. Amer. Math. Soc. 108 (1963), 275–292 and 293–312. 12.3.4, 12.3.4Google Scholar
James, D. Stasheff, Differential graded Lie algebras, quasi-Hopf algebras and higher homotopy algebras, Quantum groups (Leningrad, 1990), Lecture Notes in Math., 1510, Springer, Berlin (1992), 120–137. 14.6Google Scholar
Norman, E. Steenrod, Homology with local coefficients, Ann. of Math. (2) 44, (1943), 610–627. 1.4.6Google Scholar
Norman, E. Steenrod, A convenient category of topological spaces, Michigan Math. J. 14 (1967), 133–152. 8.5Google Scholar
Christopher, R. Stover, The equivalence of certain categories of twisted Lie and Hopf algebras over a commutative ring, J. Pure Appl. Algebra 86 (1993), no. 3, 289–326. 9.7.1Google Scholar
Sugawara, Masahiro, A condition that a space is group-like, Math. J. Okayama Univ. 7 (1957), 123–149. 12.3.4Google Scholar
Robert, M. Switzer, Algebraic topology – homotopy and homology, Reprint of the 1975 original; Classics in Mathematics. Springer-Verlag, Berlin (2002), xiv+526 pp. 2.2Google Scholar
Robert, W. Thomason, Homotopy colimits in CAT, with applications to algebraic K-theory and loop space theory, Thesis (Ph.D.) Princeton University. ProQuest LLC, Ann Arbor, MI (1977), 132 pp. 5.5.5Google Scholar
Robert, W. Thomason, Homotopy colimits in the category of small categories, Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 1, 91–109. 5.5, 9.6.5Google Scholar
Robert, W. Thomason, First quadrant spectral sequences in algebraic K-theory via homotopy colimits, Comm. Algebra 10 (1982), no. 15, 1589–1668. 11.4Google Scholar
Dieck, Tammo tom, Algebraic topology, EMS Textbooks in Mathematics. European Mathematical Society (EMS), Zürich (2008), xii+567 pp. 8.5, 8.5, 8.5.8, 8.5.10, 8.5.17Google Scholar
Rainer, M. Vogt, Convenient categories of topological spaces for homotopy theory, Arch. Math. (Basel) 22 (1971), 545–555. 8.5Google Scholar
Rainer, M. Vogt, Commuting homotopy limits, Math. Z. 153 (1977), no. 1, 59–82. 11.4.10Google Scholar
Charles, A. Weibel, An introduction to homological algebra, Cambridge Studies in Advanced Mathematics, 38. Cambridge University Press, Cambridge (1994), xiv+450 pp. (document), 10.4.1, 10.11, 16.3, 16.5, 16.5Google Scholar
Charles, A. Weibel, The K-book. An introduction to algebraic K-theory, Graduate Studies in Mathematics, 145. American Mathematical Society, Providence, RI (2013), xii+618 pp. (document), 11.3.4Google Scholar
Weiss, Michael, What does the classifying space of a category classify?, Homology Homotopy Appl. 7 (2005), no. 1, 185–195. 10.9.2Google Scholar
George, W. Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics, 61. Springer-Verlag, New York-Berlin (1978), xxi+744 pp. 1.4.6, 16.2Google Scholar
Ziegenhagen, Stephanie, En-cohomology with coefficients as functor cohomology, Algebr. Geom. Topol. 16 (2016), no. 5, 2981–3004. 15.3Google Scholar