Realizing diagrams in the homotopy category by means of diagrams of simplicial sets
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- by W. G. Dwyer and D. M. Kan PDF
- Proc. Amer. Math. Soc. 91 (1984), 456-460 Request permission
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.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 456-460
- MSC: Primary 55P15; Secondary 55U35
- DOI: https://doi.org/10.1090/S0002-9939-1984-0744648-4
- MathSciNet review: 744648