Operadic categories and 2-Segal sets

If $X$ is a 2-Segal set, then the edgewise subdivision of $X$ admits a factorization system coming from upper and lower décalage. 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.