48 citations · 172 across the 35 of their papers we have counts for
47 papers
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…
Integrals for Bialgebras
Alessandro Ardizzoni, Claudia Menini, Paolo Saracco
A well-known result by Larson and Sweedler shows that integrals on a Hopf algebra can be obtained by applying the Structure Theorem for Hopf modules to the rational part of its lin…
The binary product in the 2-category of triangular bialgebras and twisted morphisms
Alessandro Ardizzoni, Andrea Sciandra
It is well-known that the tensor product of two bialgebras constitutes the binary product in the category of cocommutative bialgebras and morphisms of bialgebras between them. In t…
On the Hopf envelope of finite-dimensional bialgebras
Alessandro Ardizzoni, Claudia Menini, Paolo Saracco
The Hopf envelope of a bialgebra is the free Hopf algebra generated by the given bialgebra. Its existence, as well as that of the cofree Hopf algebra, is a well-known fact in Hopf…
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…