Hopf Categories
E. Batista, S. Caenepeel, J. Vercruysse
TL;DR
This paper introduces Hopf categories enriched over braided monoidal categories, connecting them to recent developments in Hopf algebra theory and generalizing fundamental theorems for Hopf modules.
Contribution
It defines Hopf categories in the enriched setting and extends key theorems, bridging various concepts in Hopf algebra and category theory.
Findings
Established the notion of Hopf categories enriched over braided monoidal categories
Generalized the fundamental theorem for Hopf modules to Hopf categories
Linked Hopf categories to Hopf group (co)algebras, weak Hopf algebras, and duoidal categories
Abstract
We introduce Hopf categories enriched over braided monoidal categories. The notion is linked to several recently developed notions in Hopf algebra theory, such as Hopf group (co)algebras, weak Hopf algebras and duoidal categories. We generalize the fundamental theorem for Hopf modules and some of its applications to Hopf categories.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons