# Infinity Properads and Infinity Wheeled Properads

@inproceedings{Hackney2015InfinityPA, title={Infinity Properads and Infinity Wheeled Properads}, author={Philip Hackney and Marcy Robertson and Donald Yau}, year={2015} }

Introduction.- Graphs.- Properads.- Symmetric Monoidal Closed Structure on Properads.- Graphical Properads.- Properadic Graphical Category.- Properadic Graphical Sets and Infinity Properads.- Fundamental Properads of Infinity Properads.- Wheeled Properads and Graphical Wheeled Properads.- Infinity Wheeled Properads.- What's Next?.

## 30 Citations

Labelled cospan categories and properads

- Mathematics
- 2022

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…

On factorizations of graphical maps

- Mathematics
- 2017

We study the categories governing infinity (wheeled) properads. The graphical category, which was already known to be generalized Reedy, is in fact an Eilenberg-Zilber category. A minor alteration to…

Graphs, hypergraphs, and properads

- Mathematics
- 2014

A categorical formalism for directed graphs is introduced, featuring natural notions of morphisms and subgraphs, and leading to two elementary descriptions of the free-properad monad, first in terms…

A simplicial model for infinity properads

- Mathematics
- 2015

We show how the model structure on the category of simplicially-enriched (colored) props induces a model structure on the category of simplicially-enriched (colored) properads. A similar result holds…

On rectification and enrichment of infinity properads

- MathematicsJournal of the London Mathematical Society
- 2022

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,…

Properads and homological differential operators related to surfaces

- Mathematics
- 2019

. We give a biased definition of a properad and an explicit example of a closed Frobenius properad. We recall the construction of the cobar complex and algebra over it. We give an equivalent…

Categories of graphs for operadic structures

- Mathematics
- 2021

We recall several categories of graphs which are useful for describing homotopy-coherent versions of generalized operads (e.g. cyclic operads, modular operads, properads, and so on), and give new,…

Cospan construction of the graph category of Borisov and Manin

- MathematicsPublicacions Matemàtiques
- 2018

It is shown how the graph category of Borisov and Manin can be constructed from (a variant of) the graph category of Joyal and Kock, essentially by reversingthe generic morphisms. More precisely, the…

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