Monoidal functors, acyclic models and chain operads

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dc.creatorSantos, F. Guillen
dc.creatorNavarro, V.
dc.creatorPascual, P.
dc.creatorRoig, A.
dc.date2005-06-30
dc.date2005-10-03
dc.date.accessioned2026-07-07T06:20:30Z
dc.date.available2026-07-07T06:20:30Z
dc.descriptionWe 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.
dc.description29 pages; introduction improved, two changes in the proofs of theorems 5.3.1 and 6.3.2
dc.identifierhttps://arxiv.org/abs/math/0506624
dc.identifierhttp://arxiv.org/abs/math/0506624
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95340
dc.subjectAlgebraic Topology
dc.subjectCategory Theory
dc.subject55N40; 18G60
dc.titleMonoidal functors, acyclic models and chain operads
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