Search results for "Factorization system"

showing 2 items of 2 documents

Distributors and the comprehensive factorization system for internal groupoids

2017

In this note we prove that distributors between groupoids in a Barr-exact category epsilon form the bicategory of relations relative to the comprehensive factorization system in Gpd(epsilon). The case epsilon = Set is of special interest.

Settore MAT/02 - AlgebraMathematics::Category Theoryinternal groupoidprofunctorFOS: MathematicsMathematics - Category TheoryCategory Theory (math.CT)factorization systemdistributor18A32 20L05
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Discrete and Conservative Factorizations in Fib(B)

2021

AbstractWe focus on the transfer of some known orthogonal factorization systems from$$\mathsf {Cat}$$Catto the 2-category$${\mathsf {Fib}}(B)$$Fib(B)of fibrations over a fixed base categoryB: the internal version of thecomprehensive factorization, and the factorization systems given by (sequence of coidentifiers, discrete morphism) and (sequence of coinverters, conservative morphism) respectively. For the class of fibrewise opfibrations in$${\mathsf {Fib}}(B)$$Fib(B), the construction of the latter two simplify to a single coidentifier (respectively coinverter) followed by an internal discrete opfibration (resp. fibrewise opfibration in groupoids). We show how these results follow from thei…

Coidentifier; Coinverter; Factorization system; Internal fibrationPhysicsSequenceAlgebra and Number TheoryOrthogonal factorizationGeneral Computer ScienceInternal versionFactorization systemTheoretical Computer ScienceCombinatoricsSettore MAT/02 - AlgebraCoinverterTransfer (group theory)MorphismFactorizationInternal fibrationCoidentifierFixed baseApplied Categorical Structures
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