منابع مشابه
Separable 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...
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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...
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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...
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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.
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ژورنال
عنوان ژورنال: Journal of K-theory
سال: 2007
ISSN: 1865-2433,1865-5394
DOI: 10.1017/is007011015jkt012