1 citations · 1 across the 8 of their papers we have counts for
8 papers
Coskeletality and the higher Segal conditions
Philip Hackney
A simplicial set is -Segal if and only if it is -coskeletal and satisfies the -Segal condition in the two lowest relevant simplicial dimensions.
Embeddable partial groups
Philip Hackney, Justin Lynd, Edoardo Salati
We record a folklore theorem that says a partial group embeds in a group if and only if each word has at most one possible multiplication, regardless of choice of parenthesization.…
Models for cyclic infinity operads
Brandon Doherty, Philip Hackney
We construct model structures on cyclic dendroidal sets and cyclic dendroidal spaces for cyclic quasi-operads and complete cyclic dendroidal Segal spaces, respectively. We show the…
Higher Segal spaces and partial groups
Philip Hackney, Justin Lynd
The d-Segal conditions of Dyckerhoff and Kapranov are exactness properties for simplicial objects based on the geometry of cyclic polytopes in d-dimensional Euclidean space. 2-Sega…
The decomposition space perspective
Philip Hackney
This paper provides an introduction to decomposition spaces and 2-Segal spaces, unifying the two perspectives. We begin by defining decomposition spaces using the active-inert fact…
Dimension and partial groups
Philip Hackney, Rémi Molinier
A partial group with elements is, when regarded as a symmetric simplicial set, of dimension at most . This dimension is if and only if the partial group is a group. As…
Operadic categories and 2-Segal sets
Philip Hackney
If is a 2-Segal set, then the edgewise subdivision of admits a factorization system coming from upper and lower décalage. Using the correspondence between 2-Segal sets and…
Partial groups as symmetric simplicial sets
Philip Hackney, Justin Lynd
We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits…