3 papers
math.GR2026
On partial groups of small order
Philip Hackney
We explain a computer enumeration of all partial groups (in the sense of Chermak) of order at most 10. An accompanying dataset contains a full list, consisting of 123,650 partial g…
math.GR2026
Binary partial groups
Philip Hackney, Justin Lynd, Edoardo Salati
There are many examples of `binary' partial groups in the literature: sets equipped an identity and a partially-defined binary operation, such that each element admits an inverse.…
math.AT2025
Culf maps and edgewise subdivision
Philip Hackney, Joachim Kock
We show that, for any simplicial space , the -category of culf maps over is equivalent to the -category of right fibrations over , the…