An -hypergroupoid is a model for an n-groupoid: it is an Kan complex that is like the nerve of a groupoid (), bigroupoid () etc.
An -hypergroupoid is a Kan complex in which the horn-fillers are unique in dimension greater than :
(The lower dimensional horn fillers of course also exist, but are not in general unique.)
This is due to (Duskin 79, Glenn 82), however their definition does not ask has lower dimensional horn fillers. In Beke 04 these are called exact -types instead. For a review on the definition see (Pridham 09, section 2).
Equivalently, this are those Kan complexes which are -coskeletal and such that the -horns and -horns have unique fillers.
2-hypergroupoids are precisely the Duskin nerves of bigroupoids.
The term hypergroupoid is due to Duskin
theory_ in Applications of sheaves, number 753 in Lecture Notes in Mathematics, pages 255–279. Springer-Verlag, 1979.
and his student, Paul Glenn:
The term exact -type is used in
Presentation of higher stacks (higher geometric stacks) by hypergroupoid objects is in
Last revised on February 24, 2014 at 13:14:58. See the history of this page for a list of all contributions to it.