We characterize fibrations and (Formula presented.)-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 (Formula presented.)-fibrations from the internal version of the Gabriel–Zisman exact sequence. We also analyse fibrations and (Formula presented.)-fibrations in the category of arrows and study when the normalization functor preserves and reflects them. This analysis allows us to give a characterization of protomodular categories using strong homotopy kernels and a generalization of the Snake Lemma.
On Fibrations Between Internal Groupoids and Their Normalizations / P.-. Jacqmin, S. Mantovani, G. Metere, E.M. Vitale. - In: APPLIED CATEGORICAL STRUCTURES. - ISSN 0927-2852. - 26:5(2018 Oct 01), pp. 1015-1039.
On Fibrations Between Internal Groupoids and Their Normalizations
S. Mantovani;G. Metere;
2018
Abstract
We characterize fibrations and (Formula presented.)-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 (Formula presented.)-fibrations from the internal version of the Gabriel–Zisman exact sequence. We also analyse fibrations and (Formula presented.)-fibrations in the category of arrows and study when the normalization functor preserves and reflects them. This analysis allows us to give a characterization of protomodular categories using strong homotopy kernels and a generalization of the Snake Lemma.Pubblicazioni consigliate
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