Centers and homotopy centers in enriched monoidal categories
| Autor: | Michael Batanin, Martin Markl |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Higher category theory
Mathematics(all) Pure mathematics Deligne’s conjecture General Mathematics Mathematics::Algebraic Topology law.invention Center Hochschild complex Morphism Mathematics::K-Theory and Homology law Mathematics::Category Theory FOS: Mathematics Operads Algebraic Topology (math.AT) Monoidal categories Category Theory (math.CT) Mathematics - Algebraic Topology Mathematics Discrete mathematics Functor Homotopy Center (category theory) Mathematics - Category Theory Cofibration Invertible matrix Primary 18D10 18D20 18D50 secondary 55U40 55P48 |
| Zdroj: | Advances in Mathematics |
| ISSN: | 0001-8708 |
| DOI: | 10.1016/j.aim.2012.04.011 |
| Popis: | We consider a theory of centers and homotopy centers of monoids in monoidal categories which themselves are enriched in duoidal categories. Duoidal categories (introduced by Aguillar and Mahajan under the name 2-monoidal categories) are categories with two monoidal structures which are related by some, not necessary invertible, coherence morphisms. Centers of monoids in this sense include many examples which are not `classical.' In particular, the 2-category of categories is an example of a center in our sense. Examples of homotopy center (analogue of the classical Hochschild complex) include the Gray-category Gray of 2-categories, 2-functors and pseudonatural transformations and Tamarkin's homotopy 2-category of dg-categories, dg-functors and coherent dg-transformations. Comment: 52 pages |
| Databáze: | OpenAIRE |
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