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

Sinan Yalin (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

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.

Mots clés: operads; bialgebras category; homotopical algebra

Domaines: Topologie algébrique [math.AT]

Sinan Yalin. The homotopy theory of bialgebras over pairs of operads (research memoir). 2012. ⟨hal-00750413v2⟩