On Frobenius and separable algebra extensions in monoidal categories: applications to wreaths
نویسندگان
چکیده
منابع مشابه
Hopf Algebra Extensions and Monoidal Categories
Tannaka reconstruction provides a close link between monoidal categories and (quasi-)Hopf algebras. We discuss some applications of the ideas of Tannaka reconstruction to the theory of Hopf algebra extensions, based on the following construction: For certain inclusions of a Hopf algebra into a coquasibialgebra one can consider a natural monoidal category consisting of Hopf modules, and one can ...
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 کاملGraded Extensions of Monoidal Categories
Graded monoidal categories were introduced by Frohlich and C.T.C. ̈ Wall in 8 , where they presented a suitable abstract setting to study the Brauer group in equivariant situations. This paper is concerned with the analysis and classification of these graded monoidal categories, following a parallel treatment to that made in 2 for the non-monoidal case. In any graded monoidal category, its 1-com...
متن کاملOn Involutive Monoidal Categories
In this paper, we consider a non-posetal analogue of the notion of involutive quantale [MP92]; specifically, a (planar) monoidal category equipped with a covariant involution that reverses the order of tensoring. We study the coherence issues that inevitably result when passing from posets to categories; we also link our subject with other notions already in the literature, such as balanced mon...
متن کاملA note on the biadjunction between 2-categories of traced monoidal categories and tortile monoidal categories
We illustrate a minor error in the biadjointness result for 2-categories of traced monoidal categories and tortile monoidal categories stated by Joyal, Street and Verity. We also show that the biadjointness holds after suitably changing the definition of 2-cells. In the seminal paper “Traced Monoidal Categories” by Joyal, Street and Verity [4], it is claimed that the Int-construction gives a le...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Noncommutative Geometry
سال: 2015
ISSN: 1661-6952
DOI: 10.4171/jncg/206