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 simplifies 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).

Discrete and Conservative Factorizations in Fib(B) / A.S. Cigoli, S. Mantovani, G. Metere. - In: APPLIED CATEGORICAL STRUCTURES. - ISSN 0927-2852. - 29:2(2021 Mar), pp. 249-265. [10.1007/s10485-020-09615-9]

Discrete and Conservative Factorizations in Fib(B)

S. Mantovani
Secondo
;
G. Metere
2021

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 simplifies 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).
Coidentifier; Coinverter; Factorization system; Internal fibration;
Settore MAT/02 - Algebra
Settore MAT/04 - Matematiche Complementari
mar-2021
4-nov-2020
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/786708
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