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arXiv · 2509.26343

Double Orthogonal Factorization Systems

C. B. Aberlé·Elena Caviglia·Matthew Kukla·Rubén Maldonado·Luca Mesiti·Dorette Pronk·Tanjona Ralaivaosaona
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Abstract

We define strict and lax orthogonal factorization systems on double categories. These consist of an orthogonal factorization system on arrows and one on double cells that are compatible with each other. Our definitions are motivated by several explicit examples, including factorization systems on double categories of spans, relations and bimodules. We then prove monadicity results for orthogonal factorization systems on double categories in order to justify our definitions. For fibrant double categories we discuss the structure of the double orthogonal factorization systems that have a given orthogonal factorization system on the arrows in common. Finally, we study the interaction of orthogonal factorization systems on double categories with double fibrations.

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C. B. Aberlé, Elena Caviglia, Matthew Kukla, Rubén Maldonado, Luca Mesiti, Dorette Pronk, Tanjona Ralaivaosaona. 2025-09-30. Double Orthogonal Factorization Systems. https://arxiv.org/abs/2509.26343

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