Operadic categories and Duoidal Deligne's conjecture
| Autor: | Michael Batanin, Martin Markl |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Pure mathematics
Conjecture Statement (logic) General Mathematics Multiplicative function Monoidal category Structure (category theory) Mathematics - Category Theory 16. Peace & justice Contractible space Mathematics::Algebraic Topology Cohomology Mathematics::K-Theory and Homology Mathematics::Quantum Algebra Mathematics::Category Theory FOS: Mathematics Algebraic Topology (math.AT) Category Theory (math.CT) Mathematics - Algebraic Topology Value (mathematics) 18D10 18D20 18D50 Mathematics |
| Zdroj: | Advances in Mathematics |
| Popis: | 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. 54 pages, to appear in Advances in Mathematics |
| Databáze: | OpenAIRE |
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