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Algebraic Homotopy Theory
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1981
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