Centers and homotopy centers in enriched monoidal categories | Macquarie University ResearchOnline

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Title: Centers and homotopy centers in enriched monoidal categories
Related: Advances in mathematics, Vol. 230, No. 4-6, (2012), p.1811-1858
DOI: 10.1016/j.aim.2012.04.011
Publisher: Elsevier
Date: 2012
Author/Creator: Batanin, Michael
Author/Creator: Markl, Martin
Description: We consider a theory of centers and homotopy centers of monoids in monoidal categories which themselves are enriched in duoidal categories. The duoidal categories (introduced by Aguiar 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.
Description: 48 page(s)
Subject Keyword: Center
Subject Keyword: Deligne's conjecture
Subject Keyword: Hochschild complex
Subject Keyword: Monoidal categories
Subject Keyword: Operads
Subject Keyword: Primary
Subject Keyword: Secondary
Resource Type: journal article
Organisation: Macquarie University. Dept. of Mathematics

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