Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55P15, 55U35

Retrieve articles in all journals with MSC: 55P15, 55U35


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0744648-4
PII: S 0002-9939(1984)0744648-4
Article copyright: © Copyright 1984 American Mathematical Society