Giuseppe Metere

A push forward construction and the comprehensive factorization for internal crossed modules

In a semi-abelian category, we give a categorical construction of the push forward of an internal pre-crossed module, generalizing the pushout of a short exact sequence in abelian categories. The main properties of the push forward are discussed. A simplified version is given for action accessible categories, providing examples in the categories of rings and Lie algebras. We show that push forwards can be used to obtain the crossed module version of the comprehensive factorization for internal groupoids.

On Fibrations Between Internal Groupoids and Their Normalizations

We characterize fibrations and

Normalities and commutators

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Profunctors in Mal'tsev categories and fractions of functors

∗-fibrations in the 2-category of internal groupoids in terms of the comparison functor from certain pullbacks to the corresponding strong homotopy pullbacks. As an application, we deduce the internal version of the Brown exact sequence for

A note on strong protomodularity, actions and quotients

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Obstruction theory in action accessible categories

∗-fibrations from the internal version of the Gabriel–Zisman exact sequence. We also analyse fibrations and