Simplicial localization of monoidal structures, and a non-linear version of Deligne's conjecture

Abstract

We show that if (M, ⊗, I) is a monoidal model category then mathbb ℝEndM (I) is a (weak) 2-monoid in sSet. This applies in particular when M is the category of A-bimodules over a simplicial monoid A: the derived endomorphisms of A then form its Hochschild cohomology, which therefore becomes a simplicial 2-monoid. © Foundation Compositio Mathematica 2005.