Koszul Feynman categories

A cubical Feynman category, introduced by the authors in previous work, is a category whose functors to a base category




C

\mathcal {C}



behave like operads in




C

\mathcal {C}



. In this note we show that every cubical Feynman category is Koszul. The upshot is an explicit, minimal cofibrant resolution of any cubical Feynman category, which can be used to model




∞


\infty



versions of generalizations of operads for both graph based and non-graph based examples.