16 citations · 73 across the 20 of their papers we have counts for
22 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…
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…
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…
Categorical aspects of congruence distributivity
Michael Hoefnagel, Diana Rodelo
We study a categorical condition on relations, which is a categorical formulation of Jónsson's characterisation of congruence distributive varieties. Categories satisfying these co…
Homological lemmas for (non-abelian) group-like structures by diagram chasing in a self-dual context
Kishan Kumar Dayaram, Amartya Goswami, Zurab Janelidze +2
Through abelian categories, homological lemmas for modules admit a self-dual treatment, where half of the proof of a lemma is sufficient to prove the full lemma. In this paper, we…
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…
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…
Facets of congruence distributivity in Goursat categories
Marino Gran, Diana Rodelo, Idriss Tchoffo Nguefeu
We give new characterisations of regular Mal'tsev categories with distributive lattice of equivalence relations through variations of the so-called Triangular Lemma and Trapezoid L…
Variations of the Shifting Lemma and Goursat categories
Marino Gran, Diana Rodelo, Idriss Tchoffo Nguefeu
We prove that Mal'tsev and Goursat categories may be characterised through stronger variations of the Shifting Lemma, that is classically expressed in terms of three congruences $R…
Goursat completions
Diana Rodelo, Idriss Tchoffo Nguefeu
We characterize categories with weak finite limits whose regular completions give rise to Goursat categories.
Some remarks on connectors and groupoids in Goursat categories
Marino Gran, Diana Rodelo, Idriss Tchoffo Nguefeu
We prove that connectors are stable under quotients in any (regular) Goursat category. As a consequence, the category of connectors in is a…
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…
Beck-Chevalley condition and Goursat categories
Marino Gran, Diana Rodelo
We characterise regular Goursat categories through a specific stability property of regular epimorphisms with respect to pullbacks. Under the assumption of the existence of some pu…
Higher central extensions and cohomology
Diana Rodelo, Tim Van der Linden
We establish a Galois-theoretic interpretation of cohomology in semi-abelian categories: cohomology with trivial coefficients classifies central extensions, also in arbitrarily hig…
Some remarks on pullbacks in Gumm categories
Marino Gran, Diana Rodelo
We extend some properties of pullbacks which are known to hold in a Mal'tsev context to the more general context of Gumm categories. The varieties of universal algebras which are G…
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…
The Cuboid Lemma and Mal'tsev categories
Marino Gran, Diana Rodelo
We prove that a regular category is a Mal'tsev category if and only if a strong form of the denormalised Lemma holds true in . In this version…
On -star-permutability in regular multi-pointed categories
Marino Gran, Diana Rodelo
-star-permutable categories were introduced in a joint work with Z. Janelidze and A. Ursini as a common generalisation of regular Mal'tsev categories and of normal subtractive c…
An observation on n-permutability
Nelson Martins-Ferreira, Diana Rodelo, Tim Van der Linden
We prove that in a regular category all reflexive and transitive relations are symmetric if and only if every internal category is an internal groupoid. In particular, these condit…
Approximate Hagemann-Mitschke co-operations
Diana Rodelo, Tim Van der Linden
We show that varietal techniques based on the existence of operations of a certain arity can be extended to n-permutable categories with binary coproducts. This is achieved via wha…