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

Yalin, Sinan

Document type :

Pré-publication ou Document de travail

Title :

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

Author(s) :

Yalin, Sinan [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

English keyword(s) :

operads
bialgebras category
homotopical algebra

HAL domain(s) :

Mathématiques [math]/Topologie algébrique [math.AT]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Comment :

Research memoir, 48 pages.

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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