Homology, Homotopy and Applications

Volume 20 (2018)

Number 2

On factorizations of graphical maps

Pages: 217 – 238

DOI: https://dx.doi.org/10.4310/HHA.2018.v20.n2.a11


Philip Hackney (Department of Mathematics, Macquarie University, Sydney, New South Wales, Australia)

Marcy Robertson (School of Mathematics and Statistics, University of Melbourne, Victoria, Australia)

Donald Yau (Department of Mathematics, Ohio State University at Newark, Oh., U.S.A.)


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 the definition of the wheeled graphical category allows us to show that it is a generalized Reedy category. Finally, we present model structures for Segal properads and Segal wheeled properads.


Reedy category, graphical set, dendroidal set, Quillen model structure, Eilenberg–Zilber category, properad, wheeled properad

2010 Mathematics Subject Classification

18D50, 18G30, 18G55, 55P48, 55U35

Received 8 July 2017

Received revised 16 January 2018

Published 6 June 2018