46 citations · 197 across the 31 of their papers we have counts for
9 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…
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…
Categories of graphs for operadic structures
Philip Hackney
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…
Induced model structures for higher categories
Philip Hackney, Martina Rovelli
We give a new criterion guaranteeing existence of model structures left-induced along a functor admitting both adjoints. This works under the hypothesis that the functor induces id…
Coextension of scalars in operad theory
Gabriel C. Drummond-Cole, Philip Hackney
The functor between operadic algebras given by restriction along an operad map generally has a left adjoint. We give a necessary and sufficient condition for the restriction functo…
Modular operads and the nerve theorem
Philip Hackney, Marcy Robertson, Donald Yau
We describe a category of undirected graphs which comes equipped with a faithful functor into the category of (colored) modular operads. The associated singular functor from modula…
A criterion for existence of right-induced model structures
Gabriel C. Drummond-Cole, Philip Hackney
Suppose that is a functor whose target is a Quillen model category. We give a succinct sufficient condition for the existence of the right-induced…
On the category of props
Philip Hackney, Marcy Robertson
The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories. The titular category has nice formal properties:…