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

Joachim Kock·Bertrand Toën
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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.

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Joachim Kock, Bertrand Toën. 2003-05-12. Simplicial localization of monoidal structures, and a non-linear version of Deligne's conjecture. https://arxiv.org/abs/math/0304442

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