Operadic categories and 2-Segal sets

Philip Hackney

Operadic categories and 2-Segal sets

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arxiv 2312.00756 v1 pith:GN6MNSVB submitted 2023-12-01 math.CT math.AT

Philip Hackney This is my paper · ORCID

classification math.CTmath.AT

keywords operadicsegalcategoriesedgewisesetssubdivisionadjoinedadmits

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abstract

If $X$ is a 2-Segal set, then the edgewise subdivision of $X$ admits a factorization system coming from upper and lower d\'ecalage. Using the correspondence between 2-Segal sets and unary operadic categories satisfying the blow-up axiom, the edgewise subdivision of $X$ is interpreted as an enlargement of the associated operadic category, where fiber inclusions have been adjoined.

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