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On orthogonal factorization systems and double categories

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arxiv 2501.01363 v1 pith:4QEZFCHV submitted 2025-01-02 math.CT math.AT

Branko Juran This is my paper · ORCID
classification math.CTmath.AT
keywords inftycategoriesdoublefactorizationorthogonalsystemscategoryequivalence
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abstract

We prove that the $\infty$-category of orthogonal factorization systems embeds fully faithfully into the $\infty$-category of double $\infty$-categories. Moreover, we prove an (un)straightening equivalence for double $\infty$-categories, which restricts to an (un)straightening equivalence for op-Gray fibrations and curved orthofibrations of orthogonal factorization systems.

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  1. Pita factorisation in operadic categories

    math.CT 2025-12 conditional novelty 6.0 of 10

    For strictly factorisable operadic categories, the pita nerve is a coherent top-lax simplicial category, and a decomposition space when all quasibijections are invertible.

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