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arXiv · 1404.3886

Operadic categories and Duoidal Deligne's conjecture

Michael Batanin·Martin Markl
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Abstract

The purpose of this paper is two-fold. In Part 1 we introduce a new theory of operadic categories and their operads. This theory is, in our opinion, of an independent value. In Part 2 we use this new theory together with our previous results to prove that multiplicative 1-operads in duoidal categories admit, under some mild conditions on the underlying monoidal category, natural actions of contractible 2-operads. The result of D. Tamarkin on the structure of dg-categories, as well as the classical Deligne conjecture for the Hochschild cohomology, is a particular case of this statement.

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Michael Batanin, Martin Markl. 2014-04-15. Operadic categories and Duoidal Deligne's conjecture. https://arxiv.org/abs/1404.3886

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