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Factorization systems and double categories
Theory and applications of categories, Tome 41 (2024), pp. 551-592 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

Publié le :
Classification : 18A32, 18B10, 18M05, 18N10, 18N15
Keywords: factorization system, double category, lax morphism 
@article{TAC_2024_41_a17,
     author = {Miloslav \v{S}t\v{e}p\'an},
     title = {Factorization systems and double categories},
     journal = {Theory and applications of categories},
     pages = {551--592},
     year = {2024},
     volume = {41},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a17/}
}
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Miloslav Štěpán. Factorization systems and double categories. Theory and applications of categories, Tome 41 (2024), pp. 551-592. http://geodesic.mathdoc.fr/item/TAC_2024_41_a17/