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Title: Monoidal functors, acyclic models and chain operads
Author: Guillén Santos, Francisco
Navarro, Vicenç (Navarro Aznar)
Pascual, Pere (Pascual i Gainza)
Roig Martí, Agustí
Keywords: Àlgebra homològica
Topologia algebraica
Homological algebra
Algebraic topology
Issue Date: 1-Apr-2008
Publisher: Canadian Mathematical Society
Abstract: We prove that for a topological operad $P$ the operad of oriented cubical singular chains, $C^{\ord}_\ast(P)$, and the operad of simplicial singular chains, $S_\ast(P)$, are weakly equivalent. As a consequence, $C^{\ord}_\ast(P\nsemi\mathbb{Q})$ is formal if and only if $S_\ast(P\nsemi\mathbb{Q})$ is formal, thus linking together some formality results which are spread out in the literature. The proof is based on an acyclic models theorem for monoidal functors. We give different variants of the acyclic models theorem and apply the contravariant case to study the cohomology theories for simplicial sets defined by $R$-simplicial differential graded algebras.
It is part of: Canadian Journal of Mathematics-Journal Canadien de Mathematiques, 2008, vol. 60, p. 348-378
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ISSN: 0008-414X
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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