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math.AT2024
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…
math.GR2024
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…