# On rectification and enrichment of infinity properads

@article{Chu2022OnRA, title={On rectification and enrichment of infinity properads}, author={Hongyi Chu and Philip Hackney}, journal={Journal of the London Mathematical Society}, year={2022}, volume={105} }

We develop a theory of infinity properads enriched in a general symmetric monoidal infinity category. These are defined as presheaves, satisfying a Segal condition and a Rezk completeness condition, over certain categories of graphs. In particular, we introduce a new category of level graphs which also allow us to give a framework for algebras over an enriched infinity properad. We show that one can vary the category of graphs without changing the underlying theory. We also show that infinity…

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