3 citations · 6 across the 12 of their papers we have counts for
14 papers
Homotopy torsion theories
Sandra Mantovani, Mariano Messora, Enrico M. Vitale
In the context of categories equipped with a structure of nullhomotopies, we introduce the notion of homotopy torsion theory. As special cases, we recover pretorsion theories as we…
The third cohomology 2-group
Alan S. Cigoli, Sandra Mantovani, Giuseppe Metere
In this paper we show that a finite product preserving opfibration can be factorized through an opfibration with the same property, but with groupoidal fibres. If moreover the codo…
On pseudofunctors sending groups to 2-groups
Alan S. Cigoli, Sandra Mantovani, Giuseppe Metere
For a category B with finite products, we first characterize pseudofunctors from B to Cat whose corresponding opfibration is cartesian monoidal. Among those, we then characterize t…
Fibred categorical theory of obstruction and classification of morphisms
Alan S. Cigoli, Sandra Mantovani, Giuseppe Metere +1
We set up a fibred categorical theory of obstruction and classification of morphisms that specializes to the one of monoidal functors between categorical groups and also to the Sch…
Discrete and conservative reflections of fibrations
Alan S. Cigoli, Sandra Mantovani, Giuseppe Metere
We focus on two factorization systems for opfibrations in the 2-category Fib(B) of fibrations over a fixed base category B. The first one is the internal version of the so called c…
Galois theory and the categorical Peiffer commutator
Alan S. Cigoli, Arnaud Duvieusart, Marino Gran +1
We show that the Peiffer commutator previously defined by Cigoli, Mantovani and Metere can be used to characterize central extensions of precrossed modules with respect to the subc…
Fibered aspects of Yoneda's regular span
Alan S. Cigoli, Sandra Mantovani, Giuseppe Metere +1
In this paper we start by pointing out that Yoneda's notion of a regular span can be interpreted as a special kind of morp…
The snail lemma for internal groupoids
S. Mantovani, G. Metere, E. M. Vitale
We establish a generalized form both of the Gabriel-Zisman exact sequence associated with a pointed functor between pointed groupoids, and of the Brown exact sequence associated wi…
Bipullbacks of fractions and the snail lemma
P. -A. Jacqmin, S. Mantovani, G. Metere +1
We establish conditions giving the existence of bipullbacks in bicategories of fractions. We apply our results to construct a - exact sequence associated with a fractor b…
On fibrations between internal groupoids
P. -A. Jacqmin, S. Mantovani, G. Metere +1
In order to deduce the internal version of the Brown exact sequence from the internal version of the Gabriel-Zisman exact sequence, we characterize fibrations and -fibrations…
Peiffer product and Peiffer commutator for internal pre-crossed modules
Alan S. Cigoli, Sandra Mantovani, Giuseppe Metere
In this work we introduce the notions of Peiffer product and Peiffer commutator of internal pre-crossed modules over a fixed object B, extending the corresponding classical notions…
Butterflies in a Semi-Abelian Context
Omar Abbad, Sandra Mantovani, Giuseppe Metere +1
It is known that monoidal functors between internal groupoids in the category Grp of groups constitute the bicategory of fractions of the 2-category Grpd(Grp) of internal groupoids…
Normalities and Commutators
Sandra Mantovani, Giuseppe Metere
We first compare several algebraic notions of normality, from a categorical viewpoint. Then we introduce an intrinsic description of Higgins' commutator for ideal-determined catego…
On closure operators and reflections in Goursat categories
Francis Borceux, Marino Gran, Sandra Mantovani
By defining a closure operator on effective equivalence relations in a regular category , it is possible to establish a bijective correspondence between these closure operators…