Geodesic
The homotopy theory of strong homotopy algebras and bialgebras
Homology, homotopy, and applications, Tome 12 (2010) no. 2, pp. 39-108.

Voir la notice de l'article provenant de la source International Press of Boston

Lada introduced strong homotopy algebras to describe the structures on a deformation retract of an algebra in topological spaces. However, there is no satisfactory general definition of a morphism of strong homotopy (s.h.) algebras. Given a monad ⊤ on a simplicial category $\mathcal{C}$, we instead show how s.h. ⊤-algebras over $\mathcal{C}$ naturally form a Segal space. Given a distributive monad-comonad pair (⊤, ⊥), the same is true for s.h. (⊤,⊥)-bialgebras over $\mathcal{C}$; in particular this yields the homotopy theory of s.h. sheaves of s.h. rings. There are similar statements for quasi-monads and quasi-comonads. We also show how the structures arising are related to derived connections on bundles.
DOI : 10.4310/HHA.2010.v12.n2.a3
Classification : 18C15, 18D20, 18G30, 55U40
Keywords: algebraic theories, simplicial categories, Segal spaces 
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J. P. Pridham. The homotopy theory of strong homotopy algebras and bialgebras. Homology, homotopy, and applications, Tome 12 (2010) no. 2, pp. 39-108. doi : 10.4310/HHA.2010.v12.n2.a3. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2010.v12.n2.a3/

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