6 papers
On lax protomodularity of Ord-enriched categories
Maria Manuel Clementino, Andrea Montoli, Diana Rodelo
Our main focus concerns a possible lax version of the algebraic property of protomodularity for Ord-enriched categories. Our motivating example is the category OrdAb of preordered…
Intrinsic Schreier special objects
Andrea Montoli, Diana Rodelo, Tim Van der Linden
Motivated by the categorical-algebraic analysis of split epimorphisms of monoids, we study the concept of a special object induced by the intrinsic Schreier split epimorphisms in t…
On the categorical behaviour of -groups
Maria Manuel Clementino, Andrea Montoli
We consider compatible group structures on a -category, where is a quantale, and we study the topological and algebraic properties of such groups. Examples of such structure…
Intrinsic Schreier split extensions
Andrea Montoli, Diana Rodelo, Tim Van der Linden
In the context of regular unital categories we introduce an intrinsic version of the notion of a Schreier split epimorphism, originally considered for monoids. We show that such sp…
The 3x3 lemma in the -Maltsev and -protomodular settings. Applications to monoids and quandles
Dominique Bourn, Andrea Montoli
We investigate what is remaining of the 3x3 lemma and of the denormalized 3x3 lemma, respectively valid in a pointed protomodular and in a Maltsev category, in the context of parti…
How to centralize and normalize quandle extensions
M. Duckerts-Antoine, V. Even, A. Montoli
We show that quandle coverings in the sense of Eisermann form a (regular epi)-reflective subcategory of the category of surjective quandle homomorphisms, both by using arguments co…