Factorizable enriched categories and applications

Details Factorizable enriched categories and applications Factorizable enriched categories and applications

2011-12-04

arxiv.org/abs/1112.0781v1

Journal of Algebra, Volume 348, Issue 1, 2011, Pages 416-445

Mathematics

Category Theory

25 pages

Scientific paper

We define the twisted tensor product of two enriched categories, which generalizes various sorts of `products' of algebraic structures, including the bicrossed product of groups, the twisted tensor product of (co)algebras and the double cross product of bialgebras. The key ingredient in the definition is the notion of simple twisting systems between two enriched categories. To give examples of simple twisted tensor products we introduce matched pairs of enriched categories. Several other examples related to ordinary categories, posets and groupoids are also discussed.

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