On fibrations between internal groupoids

2017/07/04 by Pierre-Alain Jacqmin, Sandra Mantovani, Jacqmin, P. -A. +5
Mathematics · #18A22 #18A30 #18B40 #18G55 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1707.00868

openalex publication_date 2017/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ∗-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.

Citations

• The snail lemma for internal groupoids

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• The ziqqurath of exact sequences of n-groupoids