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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Homotopy coherent category theory
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by Jean-Marc Cordier and Timothy Porter PDF
Trans. Amer. Math. Soc. 349 (1997), 1-54 Request permission


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
  • Email:
  • Timothy Porter
  • Affiliation: School of Mathematics, University of Wales, Bangor, Dean Street, Bangor, Gwynedd, LL57 1UT, Wales, United Kingdom
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  • Received by editor(s): July 24, 1995
  • © Copyright 1997 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 349 (1997), 1-54
  • MSC (1991): Primary 18D20, 18D05, 18G30, 18A99
  • DOI:
  • MathSciNet review: 1376543