6533b828fe1ef96bd1288dc2

RESEARCH PRODUCT

The snail lemma for internal groupoids

Sandra MantovaniGiuseppe MetereEnrico Vitale

subject

Pure mathematicsExact sequenceLemma (mathematics)Internal groupoid Snail lemma Fibration Snake lemmaAlgebra and Number TheoryFunctorMathematics::Operator Algebras010102 general mathematicsFibrationMathematics - Category Theory01 natural sciences18B40 18D35 18G50Settore MAT/02 - AlgebraMathematics::K-Theory and HomologyMathematics::Category Theory0103 physical sciencesFOS: MathematicsCategory Theory (math.CT)Regular category010307 mathematical physics0101 mathematicsMathematics::Symplectic GeometryMathematics

description

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.

yearjournalcountryeditionlanguage
2019-10-01
http://arxiv.org/abs/1707.00875