On rectification and enrichment of infinity properads

  title={On rectification and enrichment of infinity properads},
  author={Hongyi Chu and Philip Hackney},
  journal={Journal of the London Mathematical Society},
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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