6533b833fe1ef96bd129b9ef
RESEARCH PRODUCT
On Fibrations Between Internal Groupoids and Their Normalizations
Giuseppe MetereSandra MantovaniEnrico VitalePierre-alain JacqminPierre-alain Jacqminsubject
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 physicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-05-26 | Applied Categorical Structures |