6 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…
Gabi-Monads
Sebastian Halbig, Paolo Saracco, Tony Zorman
We study gabi-monads on skew-closed categories, extending the gabi-algebras of Berger, the second author, and Vercruysse beyond the linear case. Our main reconstruction theorem ide…
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…
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…
Heaps of modules: Categorical aspects
Simion Breaz, Tomasz Brzezinski, Bernard Rybolowicz +1
Connections between heaps of modules and (affine) modules over rings are explored. This leads to explicit, often constructive, descriptions of some categorical constructions and pr…
Towards a classification of simple partial comodules of Hopf algebras
Eliezer Batista, William Hautekiet, Paolo Saracco +1
Making the first steps towards a classification of simple partial comodules, we give a general construction for partial comodules of a Hopf algebra \(H\) using central idempotents…