Factorization systems and double categories

Miloslav Štěpán

We show that factorization systems, both strict and orthogonal, can be equivalently described as double categories satisfying certain properties. This provides conceptual reasons for why the category of sets and partial maps or the category of small categories and cofunctors admit orthogonal factorization systems. The theory also gives an explicit description of various lax morphism classifiers and explains why they admit strict factorization systems.

Keywords: factorization system, double category, lax morphism

2020 MSC: 18A32, 18B10, 18M05, 18N10, 18N15

Theory and Applications of Categories, Vol. 41, 2024, No. 18, pp 551-592.

Published 2024-05-23.


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