Monoidal functors, acyclic models and chain operads

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We prove that for a topological operad $P$ the operad of oriented cubical chains, $C^{ord}_\ast(P)$, and the operad of singular chains, $S_\ast(P)$, are weakly equivalent. As a consequence, $C^{ord}_\ast(P;\mathbb{Q})$ is formal if and only if $S_\ast(P;\mathbb{Q})$ is formal, thus linking together some formality results spread 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.
29 pages; introduction improved, two changes in the proofs of theorems 5.3.1 and 6.3.2

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Algebraic Topology, Category Theory, 55N40; 18G60

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http://salesiana.dossiersoluciones.com/handle/123456789/95340

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0506624
 http://arxiv.org/abs/math/0506624

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arXiv