Operadic categories and Duoidal Deligne's conjecture
Algebraic Topology
2015-07-15 v3 Category Theory
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.
Cite
@article{arxiv.1404.3886,
title = {Operadic categories and Duoidal Deligne's conjecture},
author = {Michael Batanin and Martin Markl},
journal= {arXiv preprint arXiv:1404.3886},
year = {2015}
}
Comments
54 pages, to appear in Advances in Mathematics