We establish a generalized form both of the Gabriel-Zisman exact sequence associated with a pointed functor between pointed groupoids, and of the Brown exact sequence associated with a fibration of pointed groupoids. Our generalization consists in replacing pointed groupoids with groupoids internal to a pointed regular category with reflexive coequalizers.
The snail lemma for internal groupoids / S. Mantovani, G. Metere, E.M. Vitale. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 535(2019 Oct 01), pp. 1-34. [10.1016/j.jalgebra.2019.06.023]
The snail lemma for internal groupoids
S. Mantovani
Primo
;
2019
Abstract
We establish a generalized form both of the Gabriel-Zisman exact sequence associated with a pointed functor between pointed groupoids, and of the Brown exact sequence associated with a fibration of pointed groupoids. Our generalization consists in replacing pointed groupoids with groupoids internal to a pointed regular category with reflexive coequalizers.
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