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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Realizing diagrams in the homotopy category by means of diagrams of simplicial sets

Authors: W. G. Dwyer and D. M. Kan
Journal: Proc. Amer. Math. Soc. 91 (1984), 456-460
MSC: Primary 55P15; Secondary 55U35
MathSciNet review: 744648
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Abstract: Given a small category $ {\mathbf{D}}$, we show that a $ {\mathbf{D}}$-diagram $ \bar X$ in the homotopy category can be realized by a $ {\mathbf{D}}$-diagram of simplicial sets iff a certain simplicial set $ r\bar X$ is nonempty. Moreover, this simplicial set $ r\bar X$ can be expressed as the homotopy inverse limit of simplicial sets whose homtopy types are quite well understood. There is also an associated obstruction theory. In the special case that $ {\mathbf{D}}$ is a group (i.e. $ {\mathbf{D}}$ has only one object and all its maps are invertible) these results reduce to the ones of G. Cooke.

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PII: S 0002-9939(1984)0744648-4
Article copyright: © Copyright 1984 American Mathematical Society

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