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arXiv · 2206.00698

Labelled cospan categories and properads

Jonathan Beardsley·Philip Hackney
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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.

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Jonathan Beardsley, Philip Hackney. 2022-06-01. Labelled cospan categories and properads. https://doi.org/10.1016/j.jpaa.2023.107471

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