On Fibrations Between Internal Groupoids and Their Normalizations

被引：6

作者：

Jacqmin, P-A ^{[1
,2
]}

Mantovani, S. ^{[3
]}

Metere, G. ^{[4
]}

Vitale, E. M. ^{[1
]}

机构：

[1] Catholic Univ Louvain, Inst Rech Math & Phys, Chemin Cyclotron 2, B-1348 Louvain La Neuve, Belgium

[2] Univ Ottawa, Dept Math & Stat, King Edward 585, Ottawa, ON K1N 6N5, Canada

[3] Univ Milan, Via C Saldini 50, I-20133 Milan, Italy

[4] Univ Palermo, Dipartimento Matemat & Informat, Via Archirafi 34, I-90123 Palermo, Italy

来源：

APPLIED CATEGORICAL STRUCTURES | 2018年 / 26卷 / 05期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Internal groupoid; Fibration; Strong h-pullback; Protomodular category; SNAIL LEMMA;

D O I：

10.1007/s10485-018-9529-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1015 / 1039

页数：25

共 18 条

[1]

Borceux F., 2004, Mal'cev, protomodular, homological and semi-abelian categories

[2] 3 x 3 lemma and protomodularity [J].