46 citations · 197 across the 31 of their papers we have counts for
20 papers · 1 filter
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…
An -categorical pasting theorem
Philip Hackney, Viktoriya Ozornova, Emily Riehl +1
We show that any pasting diagram in any -category has a homotopically unique composite. This is achieved by showing that the free 2-category generated by a pasting sche…
On rectification and enrichment of infinity properads
Hongyi Chu, Philip Hackney
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 compl…
A graphical category for higher modular operads
Philip Hackney, Marcy Robertson, Donald Yau
We present a homotopy theory for a weak version of modular operads whose compositions and contractions are only defined up to homotopy. This homotopy theory takes the form of a Qui…
Dwyer--Kan homotopy theory for cyclic operads
Gabriel C. Drummond-Cole, Philip Hackney
We introduce a general definition for colored cyclic operads over a symmetric monoidal ground category, which has several appealing features. The forgetful functor from colored cyc…
Configuration spaces form a Segal semi-dendroidal space
Philip Hackney
The purpose of this short note is to illustrate the utility of (semi-) dendroidal objects in describing certain 'up-to-homotopy' operads. Specifically, we exhibit a semi-dendroidal…
On factorizations of graphical maps
Philip Hackney, Marcy Robertson, Donald Yau
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…
Lecture notes on infinity-properads
Philip Hackney, Marcy Robertson
These are notes for three lectures on higher properads given at a program at the mathematical institute MATRIX in Australia in June 2016. The first lecture covers the case of opera…
Higher cyclic operads
Philip Hackney, Marcy Robertson, Donald Yau
We introduce a convenient definition for weak cyclic operads, which is based on unrooted trees and Segal conditions. More specifically, we introduce a category of trees, which…
Shrinkability, relative left properness, and derived base change
Philip Hackney, Marcy Robertson, Donald Yau
For a connected pasting scheme , under reasonable assumptions on the underlying category, the category of -colored -props admits a cofibrantly…
A simplicial model for infinity properads
Philip Hackney, Marcy Robertson, Donald Yau
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 s…
Relative left properness of colored operads
Philip Hackney, Marcy Robertson, Donald Yau
The category of -colored symmetric operads admits a cofibrantly generated model category structure. In this paper, we show that this model structure satisfies a relat…
Infinity Properads and Infinity Wheeled Properads
Philip Hackney, Marcy Robertson, Donald Yau
A theory of -properads is developed, extending both the Joyal-Lurie -categories and the Cisinski-Moerdijk-Weiss -operads. Every connected wheel-free graph g…
Diagrams encoding group actions on -spaces
Julia E. Bergner, Philip Hackney
We introduce, for any group , a category such that diagrams satisfying a Segal condition correspond to infinite loop spaces with a -actio…
The homotopy theory of simplicial 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. In this paper, the second in a series on "higher…
Reedy categories which encode the notion of category actions
Julia E. Bergner, Philip Hackney
We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω governing category and operad structures, respectively,…
Group actions on Segal operads
Julia E. Bergner, Philip Hackney
We give a Quillen equivalence between model structures for simplicial operads, described via the theory of operads, and Segal operads, thought of as certain reduced dendroidal spac…
Homology operations and cosimplicial iterated loop spaces
Philip Hackney
If X is a cosimplical space then Tot(X) is an space and its mod 2 homology has Dyer-Lashof and Browder operations. It's natural to ask if the spec…
Spectral sequence operations converge to Araki-Kudo operations
Philip Hackney
Previously we constructed operations in the mod 2 homology spectral sequence associated to a cosimplicial E-infinity space X. The correct target for this spectral sequence is the h…
Operations in the homology spectral sequence of a cosimplicial infinite loop space
Philip Hackney
Consider the mod 2 homology spectral sequence associated to a cosimplicial space X. We construct external operations whose target is the spectral sequence associated to EΣ_2 \times…