5 citations · 10 across the 7 of their papers we have counts for
7 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 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…
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 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…
A characterization of central extensions in the variety of quandles
Valérian Even, Marino Gran, Andrea Montoli
The category of symmetric quandles is a Mal'tsev variety whose subvariety of abelian symmetric quandles is the category of abelian algebras. We give an algebraic description of the…
On the characterization of Jónsson-Tarski and of subtractive varieties
Marino Gran, Diana Rodelo
We investigate unital, subtractive and strongly unital regular categories with enough projectives and give characterizations of their projective covers. The categorical equation "s…