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Algebraic Homotopy Theory

Published online by Cambridge University Press:  20 November 2018

J. F. Jardine
J. F. Jardine*
Affiliation:
University of British Columbia, Vancouver, British Columbia
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Kan and Miller have shown in [9] that the homotopy type of a finite simplicial set K can be recovered from its R-algebra of 0-forms A0K, when R is a unique factorization domain. More precisely, if is the category of simplicial sets and is the category of R-algebras there is a contravariant functor

with

the simplicial set homomorphisms from X to the simplicial R-algebra ∇, where

and the faces and degeneracies of ∇ are induced by

and

respectively.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 2 , 01 April 1981 , pp. 302 - 319
Copyright
Copyright © Canadian Mathematical Society 1981

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