Title: On factorizations of graphical maps,
Abstract: We study the categories governing infinity (wheeled) properads. The graphical
category, which was already known to be generalized Reedy, is in fact an
Eilenberg-Zilber category. A minor alteration to the definition of the wheeled
graphical category allows us to show that it is a generalized Reedy category.
Finally, we present model structures for Segal properads and Segal wheeled
properads.