48 citations · 172 across the 35 of their papers we have counts for
15 papers · 1 filter
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…
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,…
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…
Pre-rigid Monoidal Categories
Alessandro Ardizzoni, Isar Goyvaerts, Claudia Menini
Liftable pairs of adjoint functors between braided monoidal categories in the sense of \cite{GV-OnTheDuality} provide auto-adjunctions between the associated categories of bialgebr…
Monadic vs Adjoint Decomposition
Alessandro Ardizzoni, Claudia Menini
It is known that the so-called monadic decomposition, applied to the adjunction connecting the category of bialgebras to the category of vector spaces via the tensor and the primit…
Heavily Separable Functors
Alessandro Ardizzoni, Claudia Menini
Prompted by an example related to the tensor algebra, we introduce and investigate a stronger version of the notion of separable functor that we call heavily separable. We test thi…