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Borsuk shape and a generalization of Grothendieck's definition of pro-category

Published online by Cambridge University Press:  24 October 2008

Aristide Deleanu
Affiliation:
Syracuse University, Syracuse, New York
Peter Hilton
Affiliation:
Battelle Seattle Research Center, Seattle, Washington and Case Western Reserve University, Cleveland, Ohio

Extract

Following LeVan (6), we were led in (3) to investigate a purely categorical formulation of shape theory, which had hitherto been confined to certain rather circumscribed areas of topology. However, several authors (6, 7, 8, 9, 10, 11) had noted that, within this topological context, shape theory could be related to the process of expressing objects of the larger category T as filtered limits of objects of the given full subcategory P.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

REFERENCES

(1)Artin, M. and Mazur, B.Etale Homotopy, Lecture Notes in Mathematics 100, Springer (1969).CrossRefGoogle Scholar
(2)Deleanu, A. and Hilton, P.Remark on the čech extension of cohomology functors. Proc. Adv. Study Inst. Alg. Top. Aarhus (1970), 4466.Google Scholar
(3)Deleanu, A. and Hilton, P.On the categorical shape of a functor. Fund. Math. (to appear).Google Scholar
(4)Hilton, P.On filtered systems of groups, colimits and Kan extensions. J. Pure Appl. Algebra 1 (1971), 199217.CrossRefGoogle Scholar
(5)Lee, C. and Raymond, F.čech extensions of contravariant functors. Trans. Amer. Math. Soc. 133 (1968), 415434.Google Scholar
(6)LeVan, J. Shape theory. Dissertation, University of Kentucky (1973).Google Scholar
(7)Mardešić, S.Shapes for topological spaces. General Topology and Appl. 3 (1973), 265282.CrossRefGoogle Scholar
(8)Mardešić, S.On the Whitehead theorem in shape theory. Fund. Math. (to appear).Google Scholar
(9)Mardešić, S. and Segal, J.Shapes of compacta and ANR-systems. Fund Math. 72 (1971), 4159.CrossRefGoogle Scholar
(10)Morita, K.On shapes of topological spaces. Fund. Math. (to appear).Google Scholar
(11)Weber, C.La forme d'un espace topologique est une complétion. C. R. A. Sci. Paris 277 (1973).Google Scholar