Factorization systems and double categories

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Authors

ŠTĚPÁN Miloslav

Year of publication 2024
Type Article in Periodical
Magazine / Source Theory and Applications of Categories
MU Faculty or unit

Faculty of Science

Citation
Web http://www.tac.mta.ca/tac/volumes/41/18/41-18abs.html
Keywords factorization system; double category; lax morphism
Description 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.
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