12 citations · 21 across the 15 of their papers we have counts for
19 papers
R-full Schreier internal categories and their directions
Stefano Ambra, Andrea Montoli, Diana Rodelo
We introduce the notion of R-full Schreier internal category, which is the monoid analogue of the notion of aspherical abelian groupoid. We associate with every R-full Schreier int…
A direction functor approach to the cohomology of small categories
Stefano Ambra, Arnaud Duvieusart, Andrea Montoli
We show how the direction functors can be used to develop a cohomology theory for Barr-exact and S-Maltsev categories, where S is a suitable class of split epimorphisms with a fixe…
The direction functor for Schreier extensions of monoids
Stefano Ambra, Andrea Montoli, Diana Rodelo
We observe that the process of associating an action to any Schreier extension of monoids with commutative and cancellative kernel is functorial. We show that this functor is a gen…
Algebraic exponentiation and action representability for V-groups
Maria Manuel Clementino, Andrea Montoli
We show that the category of V-groups, where V is a cartesian quantale, so in particular the category of preordered groups, is locally algebraically cartesian closed with respect t…
Torsion Theories in a Non-pointed Context
Andrea Cappelletti, Andrea Montoli
We study a non-pointed version of the notion of torsion theory in the framework of categories equipped with a posetal monocoreflective subcategory such that the coreflector inverts…
A comparison between weakly protomodular and protomodular objects in unital categories
Xabier García-Martínez, Andrea Montoli, Diana Rodelo +1
We compare the concepts of protomodular and weakly protomodular objects within the context of unital categories. Our analysis demonstrates that these two notions are generally dist…
Right-preordered groups from a categorical perspective
Maria Manuel Clementino, Andrea Montoli
We study the categorical properties of right-preordered groups, giving an explicit description of limits and colimits in this category, and studying some exactness properties. We s…
Homological Lemmas in a Non-pointed Context
Andrea Cappelletti, Andrea Montoli
We show that non-pointed versions of the classical homological lemmas hold in regular protomodular categories equipped with a suitable posetal monocoreflective subcategory. Example…
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…
On some categorical-algebraic conditions in S-protomodular categories
Nelson Martins-Ferreira, Andrea Montoli, Manuela Sobral
In the context of protomodular categories, several additional conditions have been considered in order to obtain a closer group-like behavior. Among them are locally algebraic cart…
Two characterisations of groups amongst monoids
Andrea Montoli, Diana Rodelo, Tim Van der Linden
The aim of this paper is to solve a problem proposed by Dominique Bourn: to provide a categorical-algebraic characterisation of groups amongst monoids and of rings amongst semiring…
A criterion for reflectiveness of normal extensions
Andrea Montoli, Diana Rodelo, Tim Van der Linden
We give a new sufficient condition for the normal extensions in an admissible Galois structure to be reflective. We then show that this condition is indeed fulfilled when X is the…
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…
Characteristic subobjects in semi-abelian categories
Alan S. Cigoli, Andrea Montoli
We extend to semi-abelian categories the notion of characteristic subobject, which is widely used in group theory and in the theory of Lie algebras. Moreover, we show that many of…