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math.AT2026
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.
math.AT2025
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…
math.AT2025
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…