منابع مشابه
Separable functors in corings
We develop some basic functorial techniques for the study of the categories of comodules over corings. In particular, we prove that the induction functor stemming from every morphism of corings has a left adjoint, called ad-adjoint functor. This construction generalizes the known adjunctions for the categories of Doi-Hopf modules and entwining structures. The separability of the induction and a...
متن کاملSeparable Functors and Formal Smoothness
We prove that given a bialgebra surjection π : E → H with nilpotent kernel such that H is a Hopf algebra which is formally smooth as a K-algebra, then π has a section which is a right H-colinear algebra homomorphism. Moreover, if H is also endowed with an ad-invariant integral, then the section can be chosen to be H-bicolinear. We also deal with the dual case. As an application, we prove that e...
متن کاملWhat Separable Frobenius Monoidal Functors Preserve
Abstract. Separable Frobenius monoidal functors were de ned and studied under that name in [10], [11] and [4] and in a more general context in [3]. Our purpose here is to develop their theory in a very precise sense. We determine what kinds of equations in monoidal categories they preserve. For example we show they preserve lax (meaning not necessarily invertible) Yang-Baxter operators, weak Ya...
متن کاملOn Endomorphism Algebras of Separable Monoidal Functors
We show that the (co)endomorphism algebra of a sufficiently separable “fibre” functor into Vectk, for k a field of characteristic 0, has the structure of what we call a “unital” von Neumann core in Vectk. For Vectk, this particular notion of algebra is weaker than that of a Hopf algebra, although the corresponding concept in Set is again that of a group.
متن کاملSeparable Functors for the Category of Doi-hopf Modules. Applications
We prove a Maschke type Theorem for the category of Doi-Hopf modules. In fact, we give necessary and sufficient conditions for the functor forgetting the C-coaction to be separable. This leads to a generalized notion of integrals. Our results can be applied to obtain Maschke type Theorems for Yetter-Drinfel’d modules, Long dimodules and modules graded by G-sets. Existing Maschke type Theorems d...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2020
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2019.10.008