Homotopy in functor categories

Author:
Alex Heller

Journal:
Trans. Amer. Math. Soc. **272** (1982), 185-202

MSC:
Primary 55U35; Secondary 18A25, 18G55

DOI:
https://doi.org/10.1090/S0002-9947-1982-0656485-2

Erratum:
Trans. Amer. Math. Soc. **279** (1983), 429.

MathSciNet review:
656485

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Abstract: If is a small category enriched over topological spaces the category of continuous functors from into topological spaces admits a family of homotopy theories associated with closed subcategories of . The categories , for various , are connected to one another by a functor calculus analogous to the , Hom calculus for modules over rings. The functor calculus and the several homotopy theories may be articulated in such a way as to define an analogous functor calculus on the homotopy categories. Among the functors so described are homotopy limits and colimits and, more generally, homotopy Kan extensions. A by-product of the method is a generalization to functor categories of E. H. Brown's representability theorem.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1982-0656485-2

Keywords:
Abstract homotopy,
functor category,
homotopy limit,
homotopy Kan extension,
half-exact functor

Article copyright:
© Copyright 1982
American Mathematical Society