The homotopy theory of bialgebras over pairs of operads (research memoir)

Abstract : We endow the category of coalgebras over an operad in connective non-negatively graded chain complexes with a co fibrantly generated model category structure. Then, we prove our main result : the category of bialgebras over a pair of operads (P,Q) in distribution admits a co fibrantly generated model category structure inherited from those of the P-algebras and the Q -coalgebras. This is the fi rst result of this type for a bialgebras category. It allows to do classical homotopical algebra in various categories such as associative bialgebras, Lie bialgebras or Poisson bialgebras in connective non-negatively graded chain complexes.
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Preprints, Working Papers, ...
Research memoir, 48 pages. 2012


https://hal.archives-ouvertes.fr/hal-00750413
Contributor : Sinan Yalin <>
Submitted on : Monday, November 19, 2012 - 9:39:21 PM
Last modification on : Tuesday, December 4, 2012 - 11:17:28 AM

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Sinan Yalin. The homotopy theory of bialgebras over pairs of operads (research memoir). Research memoir, 48 pages. 2012. <hal-00750413v2>

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