A categorification of the square root of -1
We give a graphical calculus for a monoidal DG category ℐ whose Grothendieck group is isomorphic to the ring ℤ[√(-1)]. We construct a categorical action of ℐ which lifts the action of ℤ[√(-1)] on ℤ².
A construction of the Hom-Yetter-Drinfeld category
In continuation of our recent work about smash product Hom-Hopf algebras [Colloq. Math. 134 (2014)], we introduce the Hom-Yetter-Drinfeld category via the Radford biproduct Hom-Hopf algebra, and prove that Hom-Yetter-Drinfeld modules can provide solutions of the Hom-Yang-Baxter equation and is a pre-braided tensor category, where (H,β,S) is a Hom-Hopf algebra. Furthermore, we show that is a Radford biproduct Hom-Hopf algebra if and only if (A,α) is a Hom-Hopf algebra in the category . Finally,...
A Maschke type theorem for relative Hom-Hopf modules
Let be a monoidal Hom-Hopf algebra and a right -Hom-comodule algebra. We first introduce the notion of a relative Hom-Hopf module and prove that the functor from the category of relative Hom-Hopf modules to the category of right -Hom-modules has a right adjoint. Furthermore, we prove a Maschke type theorem for the category of relative Hom-Hopf modules. In fact, we give necessary and sufficient conditions for the functor that forgets the -coaction to be separable. This leads to a generalized...
A note on actions of a monoidal category.
A tensor product for Gray-categories.
A universal property of the monoidal 2-category of cospans of ordinals and surjections.
Abstract physical traces.
Actions, functors and the bar construction
Adjointness between theories and strict theories
The categorical concept of a theory for algebras of a given type was foundet by Lawvere in 1963 (see [8]). Hoehnke extended this concept to partial heterogenous algebras in 1976 (see [5]). A partial theory is a dhts-category such that the object class forms a free algebra of type (2,0,0) freely generated by a nonempty set J in the variety determined by the identities ox ≈ o and xo ≈ o, where o and i are the elements selected by the 0-ary operation symbols. If the object class of a dhts-category...
Adjunctions in Monoidal categories.
An embedding theorem for Hilbert categories.
An Equivalence of Fusion Categories.
An inverse -theory functor.
Analytic functors and weak pullbacks.
Aspects of categorical algebra in initialstructure categories
Associativity constraints, braidings and quantizations of modules with grading and action.
*-autonomous categories: Once more around the track.
Bicovariant differential calculi and cross products on braided Hopf algebras
In a braided monoidal category C we consider Hopf bimodules and crossed modules over a braided Hopf algebra H. We show that both categories are equivalent. It is discussed that the category of Hopf bimodule bialgebras coincides up to isomorphism with the category of bialgebra projections over H. Using these results we generalize the Radford-Majid criterion and show that bialgebra cross products over the Hopf algebra H are precisely described by H-crossed module bialgebras. In specific braided monoidal...
Braided Groups
Braided tensor product and Lie algebra in a braided category. (Produit tensoriel tressé et algèbre de Lie dans une catégorie tressée.)