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

Abstract

We show that if $(M,\tensor,I)$ is a monoidal model category then $\REnd_M(I)$ 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.

9 pages, LaTeX; some references added

References in corpus (4)

• Operads and Motives in Deformation Quantization
• Combinatorial operad actions on cochains
• Homotopy Algebras for Operads
• Segal topoi and stacks over Segal categories

Cited by in corpus (1)

• Cohomology operations and the Deligne conjecture