Higher category theory
higher category theory
Extra properties and structure
The special case of an (n,r)-category for .
An -category, is an -category that is locally -groupoidal; that is, for any objects and , the -category is an -groupoid.
Equivalently it is an -category for which the mapping spaces are all -truncated.
- An -category with the analogous properties of a topos is an (n,1)-topos.
The canonical example of an -category is nGrpd.
In Section 11 of
the author describes a presentation of -categories by a left Bousfield localization of the model structure presenting complete Segal spaces.