Centers and homotopy centers in enriched monoidal categories
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.
Cite
@article{arxiv.1109.4084,
title = {Centers and homotopy centers in enriched monoidal categories},
author = {M. Batanin and M. Markl},
journal= {arXiv preprint arXiv:1109.4084},
year = {2012}
}
Comments
52 pages