GDO

Abstract

Spaces of homotopy coherent diagrams or of strong homotopy (s.h.) algebras (for arbitrary monads) can be realised by right-deriving sets of diagrams or of algebras. This description involves a model category generalising Leinster's homotopy monoids.

For any monad on a simplicial category, s.h. algebras thus form a Segal space. A monad on a category of deformations then yields a derived deformation functor. There are similar statements for bialgebras, giving derived deformations of schemes or of Hopf algebras.