Mal'cev, Protomodular, Homological and Semi-Abelian Categories

405 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Semidirect products and crossed modules in monoids with operations (2013, background): “Indeed, for an internal category in a category with pullbacks, being an internal groupoid is a property, which can be expressed by saying that the kernel pair of the domain morphism is given by the composition morphism and one of the projections (as showed, for example, in Proposition A.3.7 in [1]).”
On the second cohomology group in semi-abelian categories (2005, background): “pi and k is a kernel of f. Semi-abelian categories are known to provide an appropriate setting for the description of some important aspects of homological algebra, modelled on the category of groups [4]. The next property, due to Bourn, will be needed in what follows: Proposition 1.4. [6, 9] In a s”
Commutativity (2015, background): “First, we will say nothing about notions of commutativity in the context of semi-abelian categories [7].”
Higher Hopf formulae for homology via Galois Theory (2007, background): “A sequence of morphisms (fi)i∈I . . . ,2 Ai+1 fi+1 ,2 Ai fi ,2 Ai−1 ,2 . . . is called exact at Ai if Im fi+1 = Ker fi.”