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

Joachim Kock; Bertrand Toën

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

Algebraic Topology 2010-03-09 v2 Category Theory

Authors: Joachim Kock , Bertrand Toën

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.

Keywords

simplicial localization monoidal structures monoidal model category deligne's conjecture hochschild cohomology

Cite

@article{arxiv.math/0304442,
  title  = {Simplicial localization of monoidal structures, and a non-linear version of Deligne's conjecture},
  author = {Joachim Kock and Bertrand Toën},
  journal= {arXiv preprint arXiv:math/0304442},
  year   = {2010}
}

Comments

9 pages, LaTeX; some references added

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

Abstract

Keywords

Cite

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