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Homotopy coherent category theory. (English) Zbl 0865.18006

Summary: 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 generalized derived functors.

MSC:

18D20 Enriched categories (over closed or monoidal categories)
18G30 Simplicial sets; simplicial objects in a category (MSC2010)
18D05 Double categories, \(2\)-categories, bicategories and generalizations (MSC2010)
18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
18G10 Resolutions; derived functors (category-theoretic aspects)
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
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