4 papers · 1 filter
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.…
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…
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…
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…