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Operadic categories and Duoidal Deligne's conjecture

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arxiv 1404.3886 v3 pith:N47VBZHG submitted 2014-04-15 math.AT math.CT

Michael Batanin , Martin Markl This is my paper · ORCID
classification math.ATmath.CT
keywords categoriesoperadstheoryconjecturedeligneduoidaloperadicpart
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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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  1. Pita factorisation in operadic categories

    math.CT 2025-12 conditional novelty 6.0 of 10

    For strictly factorisable operadic categories, the pita nerve is a coherent top-lax simplicial category, and a decomposition space when all quasibijections are invertible.

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