On orthogonal factorization systems and double categories
Branko Juran

TL;DR
This paper establishes a deep connection between orthogonal factorization systems and double $ abla$-categories, showing a full embedding and an (un)straightening equivalence that enhances understanding of their structures.
Contribution
It proves a full embedding of orthogonal factorization systems into double $ abla$-categories and establishes an (un)straightening equivalence for these structures.
Findings
Orthogonal factorization systems fully embed into double $ abla$-categories.
An (un)straightening equivalence is established for double $ abla$-categories.
The equivalence restricts to op-Gray fibrations and curved orthofibrations.
Abstract
We prove that the -category of orthogonal factorization systems embeds fully faithfully into the -category of double -categories. Moreover, we prove an (un)straightening equivalence for double -categories, which restricts to an (un)straightening equivalence for op-Gray fibrations and curved orthofibrations of orthogonal factorization systems.
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Taxonomy
TopicsAdvanced Topics in Algebra · Rings, Modules, and Algebras · Fuzzy and Soft Set Theory
