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arXiv · 1707.00868

On fibrations between internal groupoids

P. -A. Jacqmin·S. Mantovani·G. Metere·E. M. Vitale
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Abstract

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.

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P. -A. Jacqmin, S. Mantovani, G. Metere, E. M. Vitale. 2017-07-04. On fibrations between internal groupoids. https://arxiv.org/abs/1707.00868

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