Search results for "Functor"

showing 2 items of 32 documents

The associated sheaf functor theorem in algebraic set theory

2008

We prove a version of the associated sheaf functor theorem in Algebraic Set Theory. The proof is established working within a Heyting pretopos equipped with a system of small maps satisfying the axioms originally introduced by Joyal and Moerdijk. This result improves oil the existing developments by avoiding the assumption of additional axioms for small maps and the use of collection sites.

Sheaf cohomologyFunctorDirect image functorLogicInvertible sheafIdeal sheafAlgebraMathematics::LogicDerived algebraic geometryMathematics::Category TheorySheafAlgebraic set theory presheaves sheavesInverse image functorMathematics
researchProduct

Extension theory and the calculus of butterflies

2016

Abstract This paper provides a unified treatment of two distinct viewpoints concerning the classification of group extensions: the first uses weak monoidal functors, the second classifies extensions by means of suitable H 2 -actions. We develop our theory formally, by making explicit a connection between (non-abelian) G-torsors and fibrations. Then we apply our general framework to the classification of extensions in a semi-abelian context, by means of butterflies [1] between internal crossed modules. As a main result, we get an internal version of Dedecker's theorem on the classification of extensions of a group by a crossed module. In the semi-abelian context, Bourn's intrinsic Schreier–M…

TorsorCrossed moduleContext (language use)01 natural sciencesCohomologyCohomology; Extension; Fibrations; Obstruction theory; Schreier-mac lane theorem; TorsorsExtensionMathematics::Category Theory0103 physical sciences0101 mathematicsConnection (algebraic framework)MathematicsAlgebra and Number TheoryFunctorGroup (mathematics)010102 general mathematicsTorsorsExtension (predicate logic)Obstruction theorySchreier-mac lane theoremCohomologyFibrationsAlgebraSettore MAT/02 - AlgebraSchreier–Mac Lane theoremSettore MAT/03 - Geometria010307 mathematical physicsObstruction theory
researchProduct