Homotopy in functor categories
Author:
Alex Heller
Journal:
Trans. Amer. Math. Soc. 272 (1982), 185202
MSC:
Primary 55U35; Secondary 18A25, 18G55
Erratum:
Trans. Amer. Math. Soc. 279 (1983), 429.
MathSciNet review:
656485
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Abstract 
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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 byproduct of the method is a generalization to functor categories of E. H. Brown's representability theorem.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198206564852
PII:
S 00029947(1982)06564852
Keywords:
Abstract homotopy,
functor category,
homotopy limit,
homotopy Kan extension,
halfexact functor
Article copyright:
© Copyright 1982
American Mathematical Society
