Semidirect products of categorical groups. Obstruction theory.
Semigroups with S.M.F. structures.
Separable and Frobenius monoidal Hom-algebras
As generalizations of separable and Frobenius algebras, separable and Frobenius monoidal Hom-algebras are introduced. They are all related to the Hom-Frobenius-separability equation (HFS-equation). We characterize these two Hom-algebraic structures by the same central element and different normalizing conditions, and the structure of these two types of monoidal Hom-algebras is studied. The Nakayama automorphisms of Frobenius monoidal Hom-algebras are considered.
Separable functors for the category of Doi Hom-Hopf modules
Let be the category of Doi Hom-Hopf modules, be the category of A-Hom-modules, and F be the forgetful functor from to . The aim of this paper is to give a necessary and suffcient condition for F to be separable. This leads to a generalized notion of integral. Finally, applications of our results are given. In particular, we prove a Maschke type theorem for Doi Hom-Hopf modules.
Serre Theorem for involutory Hopf algebras
We call a monoidal category C a Serre category if for any C, D ∈ C such that C ⊗ D is semisimple, C and D are semisimple objects in C. Let H be an involutory Hopf algebra, M, N two H-(co)modules such that M ⊗ N is (co)semisimple as a H-(co)module. If N (resp. M) is a finitely generated projective k-module with invertible Hattory-Stallings rank in k then M (resp. N) is (co)semisimple as a H-(co)module. In particular, the full subcategory of all finite dimensional modules, comodules or Yetter-Drinfel’d...
Sesqui-monades et monades locales
Shape Invariant Functors: Application in Module-Theory.
Shape theory in a bicategory
Sheaves and Cauchy-complete categories
Sheaves for an involutive quantaloid
Shellability of a poset of polygonal subdivisions.
Shuffle bialgebras
The goal of our work is to study the spaces of primitive elements of some combinatorial Hopf algebras, whose underlying vector spaces admit linear basis labelled by subsets of the set of maps between finite sets. In order to deal with these objects we introduce the notion of shuffle algebras, which are coloured algebras where composition is not always defined. We define bialgebras in this framework and compute the subpaces of primitive elements associated to them. These spaces of primitive elements...
Simplicial matrices and the nerves of weak -categories I: Nerves of bicategories.
Simplicial -fold monoidal categories model all loop spaces
Simultaneously reflective and coreflective subcategories of presheaves.
Skew-monoidal structures on simple rings with several objects.
Small-fibred semitopological functors without small-fibred initial completions
Smash (co)products and skew pairings.
Let τ be an invertible skew pairing on (B,H) where B and H are Hopf algebras in a symmetric monoidal category C with (co)equalizers. Assume that H is quasitriangular. Then we obtain a new algebra structure such that B is a Hopf algebra in the braided category HHγD and there exists a Hopf algebra isomorphism w: B ∞ H → B [×]τ H in C, where B ∞ H is a Hopf algebra with (co)algebra structure the smash (co)product and B [×]τ H is the Hopf algebra defined by Doi and Takeuchi.
Some algebraic applications of graded categorical group theory.
Some remarks on the subject of coherence