The homotopy theory of bialgebras over ...
Document type :
Article dans une revue scientifique: Article original
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Title :
The homotopy theory of bialgebras over pairs of operads
Author(s) :
Journal title :
Journal of Pure and Applied Algebra
Pages :
973-991
Publisher :
Elsevier
Publication date :
2014-06-01
ISSN :
0022-4049
English keyword(s) :
operads
bialgebras category
homotopical algebra
bialgebras category
homotopical algebra
HAL domain(s) :
Mathématiques [math]/Topologie algébrique [math.AT]
English abstract : [en]
We endow the category of bialgebras over a pair of operads in distribution with a cofibrantly generated model category structure. We work in the category of chain complexes over a field of characteristic zero. We split our ...
Show more >We endow the category of bialgebras over a pair of operads in distribution with a cofibrantly generated model category structure. We work in the category of chain complexes over a field of characteristic zero. We split our construction in two steps. In the first step, we equip coalgebras over an operad with a cofibrantly generated model category structure. In the second one we use the adjunction between bialgebras and coalgebras via the free algebra functor. This result allows us to do classical homotopical algebra in various categories such as associative bialgebras, Lie bialgebras or Poisson bialgebras in chain complexes.Show less >
Show more >We endow the category of bialgebras over a pair of operads in distribution with a cofibrantly generated model category structure. We work in the category of chain complexes over a field of characteristic zero. We split our construction in two steps. In the first step, we equip coalgebras over an operad with a cofibrantly generated model category structure. In the second one we use the adjunction between bialgebras and coalgebras via the free algebra functor. This result allows us to do classical homotopical algebra in various categories such as associative bialgebras, Lie bialgebras or Poisson bialgebras in chain complexes.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
Comment :
27 pages, final version.
Collections :
Source :
Submission date :
2025-01-24T10:11:29Z
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