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.

Final author version, to appear in HHA

Cited by in corpus (5)

• A graphical category for higher modular operads
• Modular operads and the nerve theorem
• On rectification and enrichment of infinity properads
• Categories of graphs for operadic structures
• Segal conditions for generalized operads