Labelled cospan categories and properads

Abstract

We prove Steinebrunner's conjecture on the biequivalence between (colored) properads and labelled cospan categories. The main part of the work is to establish a 1-categorical, strict version of the conjecture, showing that the category of properads is equivalent to a category of strict labelled cospan categories via the symmetric monoidal envelope functor.

arXiv comment63 pages. v2: Several updates based on suggestions from a referee

References in corpus (8)

• A Koszul duality for props
• Homotopy theory for algebras over polynomial monads
• Infinity Properads and Infinity Wheeled Properads
• Categorical notions of fibration
• Corelations are the prop for extraspecial commutative Frobenius monoids
• On the category of props
• The homotopy theory of simplicial props
• On rectification and enrichment of infinity properads

Cited by in corpus (2)

• Categories of graphs for operadic structures
• The equifibered approach to $\infty$-properads