Labelled cospan categories and properads
Category Theory
2023-08-21 v2 Algebraic Topology
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.
Cite
@article{arxiv.2206.00698,
title = {Labelled cospan categories and properads},
author = {Jonathan Beardsley and Philip Hackney},
journal= {arXiv preprint arXiv:2206.00698},
year = {2023}
}
Comments
63 pages. v2: Several updates based on suggestions from a referee