Bimonads and Hopf monads on categories
By Bachuki Mesablishvili, Robert Wisbauer. 2007
62 citations recorded by the source corpus.
The purpose of this paper is to develop a theory of bimonads and Hopf monads on arbitrary categories thus providing the possibility to transfer the essentials of the theory of Hopf algebras in vector spaces to more general settings. There are several extensions of this theory to monoidal categories which in a certain sense follow the classical trace. Here we do not pose any conditions on our base category but we do refer to the monoidal structure of the category of endofunctors on any category A and by this we retain some of the combinatorial complexity which makes the theory so interesting. As a basic tool we use distributive laws between monads and comonads (entwinings) on A: we define a bimonad on A as an endofunctor B which �
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6fbd74f5c49732a13bb14e4f6dcc18c0318fbdd5
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In Algebra and Number Theory
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Citations in the corpus
- Skew-monoidal categories and bialgebroids (2012, background): “The compatibility condition between the R-ring and the R-coring structure is too complicated to witness about something fundamental which may motivate to search for other generalizations of bialgebras [18].”
- MONADS AND COMONADS ON MODULE CATEGORIES (2008, background): “(2) The (co)free functor − ⊗A C is right adjoint to the forgetful functor by the isomorphism HomC(M,X ⊗A C) → HomA(M,X), f 7→ (IX ⊗A ε) ◦ f. (3) For any generator P ∈ MA, P ⊗A C is a subgenerator in M C, in particular, C is a subgenerator in MC. (4) For any cogenerator Q ∈ MA, Q⊗A C is a cogenerator”