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
Mantovani, S., Metere, G., Vitale, E.M. (2019). The snail lemma for internal groupoids. JOURNAL OF ALGEBRA, 535(-), 1-34 [10.1016/j.jalgebra.2019.06.023].
The snail lemma for internal groupoids
Metere, Giuseppe;
2019-01-01
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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