5 papers
Central series of cocommutative Hopf braces
Maria Bevilacqua, Marino Gran, Andrea Sciandra
By extending some classical results known for groups and skew braces, we define and investigate central series of cocommutative Hopf braces. Both left and right central series are…
Hopf formulae for cocommutative Hopf algebras
Marino Gran, Andrea Sciandra
The adjunction between coalgebras and Hopf algebras, first described by Takeuchi, allows one to prove that the semi-abelian category of cocommutative Hopf algebras has enough $\mat…
Hopf formulae for homology of skew braces
M. Gran, T. Letourmy, L. Vendramin
The variety of skew braces contains several interesting subcategories as subvarieties, as for instance the varieties of radical rings, of groups and of abelian groups. In this arti…
Double groupoids and -groupoids in regular Mal'tsev categories
Nadja Egner, Marino Gran
We prove that the category 2- of internal -groupoids is a Birkhoff subcategory of the category of double groupoids…
Hopf braces and semi-abelian categories
Marino Gran, Andrea Sciandra
Hopf braces have been introduced as a Hopf-theoretic generalization of skew braces. Under the assumption of cocommutativity, these algebraic structures are equivalent to matched pa…