Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-11T11:17:40.677Z Has data issue: false hasContentIssue false
  • English
  • Français

Traced monoidal categories

Published online by Cambridge University Press:  24 October 2008

André Joyal ,
Ross Street  and
Dominic Verity
André Joyal
Affiliation:
Département de Mathématiques, Université du Québec à Montréal, Montréal, Québec H3C 3P8, Canada
Ross Street
Affiliation:
School of Mathematics, Physics, Computing & Electronics, Macquarie University, New South Wales 2109, Australia
Dominic Verity
Affiliation:
School of Mathematics, Physics, Computing & Electronics, Macquarie University, New South Wales 2109, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

Traced monoidal categories are introduced, a structure theorem is proved for them, and an example is provided where the structure theorem has application.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 3 , April 1996 , pp. 447 - 468
Copyright
Copyright © Cambridge Philosophical Society 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[BÉ]Bloom, S. L. and Ésik, Z.. Iteration theories. EATCS Monographs on Theoretical Computer Science (Springer-Verlag, 1993).Google Scholar
[CJSV]Carboni, A., Johnson, S., Street, R. and Verity, D.. Modulated bicategories. J. Pure Appl. Algebra 94 (1994), 229–282.CrossRefGoogle Scholar
[FY1]Freyd, P. and Yetter, D.. Braided compact closed categories with applications to low dimensional topology. Advances in Math. 77 (1989). 156–182.CrossRefGoogle Scholar
[FY2]Freyd, P. and Yetter, D.. Coherence theorems via knot theory. J. Pure Appl. Algebra 78 (1992), 49–76.CrossRefGoogle Scholar
[G]Girard, J.-Y.. Geometry of interaction I, interpretation of system F. Stud. Logic, Found. Math. 127 (1989), 221–260.CrossRefGoogle Scholar
[JS1]Joyal, A. and Street, R.. Braided tensor categories. Advances in Math. 102 (1993), 20–78.CrossRefGoogle Scholar
[JS2]Joyal, A. and Street, R.. The geometry of tensor calculus I. Advances in Math. 88 (1991), 55–113.CrossRefGoogle Scholar
[JS3]Joyal, A. and Street, R.. Tortile Yang-Baxter operators in tensor categories. J. Pure Appl. Algebra 71 (1991), 43–51.CrossRefGoogle Scholar
[JS4]Joyal, A. and Street, R.. An introduction to Tannaka duality and quantum groups; in Category Theory. Proceedings, Como 1990; Part II of Lecture Notes in Math. 1488 (Springer-Verlag, 1991), 411–492.Google Scholar
[JS5]Joyal, A. and Street, R.. The geometry of tensor calculus II (in preparation).Google Scholar
[K.L]Kelly, G. M. and Laplaza, M. L.. Coherence for compact closed categories. J. Pure Appl. Algebra 19 (1980), 193–213.CrossRefGoogle Scholar
[ML]Maclane, S.. Categories for the working mathematician (Springer-Verlag, 1971).Google Scholar
[RT]Reshetikhin, N. Yu. and Turaev, V. G.. Ribbon graphs and their invariants derived from quantum groups. Comm. Math. Phys. 127 (1) (1990), 1–26.CrossRefGoogle Scholar
[SR]Rivano, N. Saavedra. Catégories Tannakiennes. Lecture Notes in Math. 265 (Springer-Verlag, 1972).Google Scholar
[Sm]Chee, Shum Mei. Tortile tensor categories (PhD thesis, Macquarie University, November 1989). J. Pure Appl. Algebra 93 (1994), 57–110.CrossRefGoogle Scholar
[Y]Yetter, D. N.. Markov algebras. Contemporary Math. 78 (1988), 705–730.CrossRefGoogle Scholar