Classifying spaces of algebras over a prop
Document type :
Article dans une revue scientifique: Article original
Permalink :
Title :
Classifying spaces of algebras over a prop
Author(s) :
Journal title :
Algebraic and Geometric Topology
Pages :
2561-2593
Publisher :
Mathematical Sciences Publishers
Publication date :
2014-11-05
ISSN :
1472-2747
English keyword(s) :
bialgebras category
classifying space
homotopy invariance
prop
classifying space
homotopy invariance
prop
HAL domain(s) :
Mathématiques [math]/Topologie algébrique [math.AT]
English abstract : [en]
We prove that a weak equivalence between cofibrant props induces a weak equivalence between the associated classifying spaces of algebras. This statement generalizes to the prop setting a homotopy invariance result which ...
Show more >We prove that a weak equivalence between cofibrant props induces a weak equivalence between the associated classifying spaces of algebras. This statement generalizes to the prop setting a homotopy invariance result which is well known in the case of algebras over operads. The absence of model category structure on algebras over a prop leads us to introduce new methods to overcome this difficulty. We also explain how our result can be extended to algebras over colored props in any symmetric monoidal model category tensored over chain complexes.Show less >
Show more >We prove that a weak equivalence between cofibrant props induces a weak equivalence between the associated classifying spaces of algebras. This statement generalizes to the prop setting a homotopy invariance result which is well known in the case of algebras over operads. The absence of model category structure on algebras over a prop leads us to introduce new methods to overcome this difficulty. We also explain how our result can be extended to algebras over colored props in any symmetric monoidal model category tensored over chain complexes.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
Collections :
Source :
Submission date :
2025-01-22T07:16:24Z
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