Discrete and Conservative Factorizations in Fib(B)

Giuseppe Metere, Alan S. Cigoli, Sandra Mantovani

Risultato della ricerca: Articlepeer review

Abstract

We focus on the transfer of some known orthogonal factorization systems from Cat to the 2-category Fib(B) of fibrations over a fixed base category B: the internal version of the comprehensive 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 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 their analogues in Cat, providing suitable conditions on a 2-category C, that allow the transfer of the construction of coinverters and coidentifiers from C to FibC(B).
Lingua originaleEnglish
pagine (da-a)249-265
Numero di pagine17
RivistaApplied Categorical Structures
Volume29
Stato di pubblicazionePublished - 2021

All Science Journal Classification (ASJC) codes

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  • ???subjectarea.asjc.1700.1700???

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