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Transactions of the American Mathematical Society

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Homotopy coherent category theory

Authors: Jean-Marc Cordier and Timothy Porter
Journal: Trans. Amer. Math. Soc. 349 (1997), 1-54
MSC (1991): Primary 18D20, 18D05, 18G30, 18A99
MathSciNet review: 1376543
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Abstract: This article is an introduction to the categorical theory of homotopy coherence. It is based on the construction of the homotopy coherent analogues of end and coend, extending ideas of Meyer and others. The paper aims to develop homotopy coherent analogues of many of the results of elementary category theory, in particular it handles a homotopy coherent form of the Yoneda lemma and of Kan extensions. This latter area is linked with the theory of generalised derived functors.

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Additional Information

Jean-Marc Cordier
Affiliation: Faculté de Mathématiques et d’Informatique, Université de Picardie - Jules Verne, 33 rue Saint Leu, 80039 Amiens Cédex 1, France

Timothy Porter
Affiliation: School of Mathematics, University of Wales, Bangor, Dean Street, Bangor, Gwynedd, LL57 1UT, Wales, United Kingdom

Keywords: Simplicially enriched categories, homotopy coherent ends and coends, Yoneda lemma
Received by editor(s): July 24, 1995
Article copyright: © Copyright 1997 American Mathematical Society