0000000000686844

AUTHOR

Pierre-alain Jacqmin

showing 2 related works from this author

Bipullbacks of fractions and the snail lemma

2017

Abstract 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.

Pure mathematicsLemma (mathematics)Exact sequenceInternal groupoidAlgebra and Number Theory010102 general mathematicsMathematics - Category TheoryBicategory of fraction18B40 18D05 18E35 18G5001 natural sciencesMathematics::Algebraic TopologySettore MAT/02 - AlgebraExact categoryMathematics::K-Theory and HomologyMathematics::Category Theory0103 physical sciencesFOS: MathematicsBipullbackSnail lemmaCategory Theory (math.CT)010307 mathematical physics0101 mathematicsMathematics
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On Fibrations Between Internal Groupoids and Their Normalizations

2018

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. As an application, we deduce the internal version of the Brown exact sequence for $$*$$ -fibrations from the internal version of the Gabriel–Zisman exact sequence. We also analyse fibrations and $$*$$ -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.

Normalization (statistics)Pure mathematicsInternal groupoid Fibration Strong h-pullback Protomodular categoryGeneral Computer ScienceFibrationSnake lemmaStrong h-pullbackMathematics::Algebraic Topology01 natural sciencesTheoretical Computer ScienceMathematics::Algebraic GeometryMathematics::K-Theory and HomologyMathematics::Category Theory0103 physical sciences0101 mathematicsMathematics::Symplectic GeometryMathematicsExact sequenceInternal groupoidAlgebra and Number TheoryFunctorHomotopy010102 general mathematicsFibrationInternal versionSettore MAT/02 - AlgebraProtomodular categoryTheory of computation010307 mathematical physicsApplied Categorical Structures
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