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arXiv · 1109.4084

Centers and homotopy centers in enriched monoidal categories

M. Batanin·M. Markl
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Abstract

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.

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M. Batanin, M. Markl. 2011-09-19. Centers and homotopy centers in enriched monoidal categories. https://arxiv.org/abs/1109.4084

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