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Koszul Feynman Categories (2108.09251v2)
Published 20 Aug 2021 in math.AT and math.CT
Abstract: A cubical Feynman category, introduced by the authors in previous work, is a category whose functors to a base category $\mathcal{C}$ behave like operads in $\mathcal{C}$. 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.
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