2 citations · 2 across the 7 of their papers we have counts for
8 papers
Frobenius functors and one-sided Hopf algebras in braided monoidal categories
Lucrezia Bottegoni, Davide Ferri, Paolo Saracco
Evidence suggests a tight connection between the existence of antipode-like maps on bialgebra-like structures, and the Frobenius property for the associated free Hopf module functo…
Protomodularity of cocommutative Hopf monoids in duoidal categories and quasitriangular Hopf algebras
Alessandro Ardizzoni, Lucrezia Bottegoni, Alan Cigoli +1
In this work, we extend the protomodularity of the category of cocommutative Hopf algebras to the quasitriangular setting. Every quasitriangular Hopf algebra admits a minimal quasi…
Semiseparability of induction functors in a monoidal category
Lucrezia Bottegoni, Zhenbang Zuo
For any algebra morphism in a monoidal category, we provide sufficient conditions (which are also necessary if the unit is a left tensor generator) for the attached induction funct…
Infinitesimal -matrices for some families of Hopf algebras
Lucrezia Bottegoni, Fabio Renda, Andrea Sciandra
Given a bialgebra such that the associated trivial topological bialgebra admits a quasitriangular structure $\tilde{\mathcal{R}}=\mathcal{R}(1\otimes 1+\hbarχ+\mat…
On (naturally) semifull and (semi)separable semifunctors
Lucrezia Bottegoni
The notion of semifunctor between categories, due to S. Hayashi (1985), is defined as a functor that does not necessarily preserve identities. In this paper we study how several pr…
Semiseparable functors and conditions up to retracts
Alessandro Ardizzoni, Lucrezia Bottegoni
In a previous paper we introduced the concept of semiseparable functor. Here we continue our study of these functors in connection with idempotent (Cauchy) completion. To this aim,…
Infinitesimal braidings and pre-Cartier bialgebras
A. Ardizzoni, L. Bottegoni, A. Sciandra +1
We propose an infinitesimal counterpart to the notion of braided category. The corresponding infinitesimal braidings are natural transformations which are compatible with an underl…
Semiseparable functors
Alessandro Ardizzoni, Lucrezia Bottegoni
In this paper we introduce and investigate the notion of semiseparable functor. One of its first features is that it allows a novel description of separable and naturally full func…