Reference : The homotopy theory of bialgebras over pairs of operads
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/22421
The homotopy theory of bialgebras over pairs of operads
English
Yalin, Sinan mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2014
Journal of Pure and Applied Algebra
Elsevier Science
218
6
973-991
Yes (verified by ORBilu)
International
0022-4049
1873-1376
[en] operads ; bialgebras ; homotopical algebra
[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 construction in two steps. In the first step, we equip coalgebras over an operad with a cofibrantly generated model category structure. In the second step 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.
http://hdl.handle.net/10993/22421

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