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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.GR2026
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.…