8 citations · 14 across the 14 of their papers we have counts for
18 papers
Coherent and ideal actions in ideally exact categories
Manuel Mancini, Giuseppe Metere, Federica Piazza
In the context of ideally exact categories, we introduce the notions of internal coherent action and internal ideal action that generalise different aspects of unital actions of ri…
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 the representability of actions of Leibniz algebras and Poisson algebras
Alan S. Cigoli, Manuel Mancini, Giuseppe Metere
In a recent paper, motivated by the study of central extensions of associative algebras, G. Janelidze introduces the notion of weakly action representable category. In this paper,…
Relative ideals in homological categories, with an application to MV-algebras
Serafina Lapenta, Giuseppe Metere, Luca Spada
Let be a homological category and be a faithful conservative right adjoint. We introduce the notion of relative ideal with respect to , and we show that, un…
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…
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…
Distributors and the comprehensive factorization system for internal groupoids
Giuseppe Metere
In this note we prove that distributors between groupoids in a Barr-exact category E form the bicategory of relations relative to the comprehensive factorization system in Gpd(E).…
Bourn-normal monomorphisms in regular Mal'tsev categories
Giuseppe Metere
Normal monomorphisms in the sense of Bourn describe the equivalence classes of an internal equivalence relation. Although the definition is given in the fairly general setting of a…
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…
A note on strong protomodularity, actions and quotients
Giuseppe Metere
In order to study the problems of extending an action along a quotient of the acted object and along a quotient of the acting object, we investigate some properties of the fibratio…
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…
The ziqqurath of exact sequences of n-groupoids
Giuseppe Metere
Higher Dimensional Categories are showing relevant implications in several fields of mathematical research. Nevertheless basic algebraic tools, in order to further develop the theo…