Operadic categories and duoidal Deligne's conjecture

Michael Batanin, Martin Markl*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)1630-1687
    Number of pages58
    JournalAdvances in Mathematics
    Volume285
    DOIs
    Publication statusPublished - 5 Nov 2015

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