  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.
