46 citations · 197 across the 31 of their papers we have counts for
4 papers · 1 filter
Free decomposition spaces
Philip Hackney, Joachim Kock
We introduce the notion of free decomposition spaces: they are simplicial spaces freely generated by their inert maps. We show that left Kan extension along the inclusion $j \colon…
Culf maps and edgewise subdivision
Philip Hackney, Joachim Kock
We show that, for any simplicial space , the -category of culf maps over is equivalent to the -category of right fibrations over , the…
Segal conditions for generalized operads
Philip Hackney
This note is an introduction to several generalizations of the dendroidal sets of Moerdijk--Weiss. Dendroidal sets are presheaves on a category of rooted trees, and here we conside…
Labelled cospan categories and properads
Jonathan Beardsley, Philip Hackney
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, stri…