Search results for "Bicategory of fraction"

showing 2 items of 2 documents

Butterflies in a Semi-Abelian Context

2011

It is known that monoidal functors between internal groupoids in the category Grp of groups constitute the bicategory of fractions of the 2-category Grpd(Grp) of internal groupoids, internal functors and internal natural transformations in Grp, with respect to weak equivalences (that is, internal functors which are internally fully faithful and essentially surjective on objects). Monoidal functors can be equivalently described by a kind of weak morphisms introduced by B. Noohi under the name of butterflies. In order to internalize monoidal functors in a wide context, we introduce the notion of internal butterflies between internal crossed modules in a semi-abelian category C, and we show th…

Discrete mathematicsPure mathematicsButterflyFunctorInternal groupoidWeak equivalenceGeneral MathematicsSemi-abelian categoryFunctor categoryContext (language use)Mathematics - Category TheoryBicategory of fractionBicategoryMathematics::Algebraic TopologyWeak equivalence18D05 18B40 18E10 18A40Surjective functionMorphismMathematics::Category TheoryFOS: MathematicsCategory Theory (math.CT)Abelian groupMathematics
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Bipullbacks of fractions and the snail lemma

2017

Abstract We establish conditions giving the existence of bipullbacks in bicategories of fractions. We apply our results to construct a π 0 - π 1 exact sequence associated with a fractor between groupoids internal to a pointed exact category.

Pure mathematicsLemma (mathematics)Exact sequenceInternal groupoidAlgebra and Number Theory010102 general mathematicsMathematics - Category TheoryBicategory of fraction18B40 18D05 18E35 18G5001 natural sciencesMathematics::Algebraic TopologySettore MAT/02 - AlgebraExact categoryMathematics::K-Theory and HomologyMathematics::Category Theory0103 physical sciencesFOS: MathematicsBipullbackSnail lemmaCategory Theory (math.CT)010307 mathematical physics0101 mathematicsMathematics
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