Bimonads and Hopf monads on categories
نویسندگان
چکیده
منابع مشابه
Bimonads and Hopf Monads on Categories
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 ba...
متن کاملNotes on Bimonads and Hopf Monads
For a generalisation of the classical theory of Hopf algebra over fields, A. Bruguières and A. Virelizier study opmonoidal monads on monoidal categories (which they called bimonads). In a recent joint paper with S. Lack the same authors define the notion of a pre-Hopf monad by requiring only a special form of the fusion operator to be invertible. In previous papers it was observed by the presen...
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The theory of monads on categories equipped with a dagger (a contravariant identity-on-objects involutive endofunctor) works best when all structure respects the dagger: the monad and adjunctions should preserve the dagger, and the monad and its algebras should satisfy the so-called Frobenius law. Then any monad resolves as an adjunction, with extremal solutions given by the categories of Kleis...
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Let A be a ring and MA the category of right A-modules. It is well known in module theory that any A-bimodule B is an A-ring if and only if the functor − ⊗A B : MA → MA is a monad (or triple). Similarly, an A-bimodule C is an A-coring provided the functor − ⊗A C : MA → MA is a comonad (or cotriple). The related categories of modules (or algebras) of −⊗A B and comodules (or coalgebras) of − ⊗A C...
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Introduction The development of the formal theory of monads, begun in [23] and continued in [15], shows that much of the theory of monads [1] can be generalized from the setting of the 2-category Cat of small categories, functors and natural transformations to that of a general 2-category. The generalization, which involves defining the 2-category Mnd(K) of monads, monad maps and monad 2-cells ...
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ژورنال
عنوان ژورنال: Journal of K-Theory
سال: 2010
ISSN: 1865-2433,1865-5394
DOI: 10.1017/is010001014jkt105