arXiv subjects

S. Mantovani

Publications and source records attributed to S. Mantovani.

3 recordsLinked to original sources

arXiv2017

On fibrations between internal groupoids

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 $\ast$-fibrations in the 2-category of internal groupoids in terms of the comparison functor from certain pullbacks to the corresponding strong homotopy pullbacks. A similar analysis in the category of arrows allows us to give a characterization of protomodular categories using strong homotopy kernels.

math.CT↗

arXiv2017

Bipullbacks of fractions and the snail lemma

We establish conditions giving the existence of bipullbacks in bicategories of fractions. We apply our results to construct a $π_0$-$π_1$ exact sequence associated with a fractor between groupoids internal to a pointed exact category.

math.CT↗

arXiv2017

The snail lemma for internal groupoids

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 with a fibration of pointed groupoids. Our generalization consists in replacing pointed groupoids with groupoids internal to a pointed regular category with reflexive coequalizers.

math.CT↗