(2,1)-quasitopos?
structures in a cohesive (∞,1)-topos
For a locally ∞-connected (∞,1)-topos and an object, we say that is the fundamental -groupoid of in .
This is the object that encodes the geometric homotopy groups in an (∞,1)-topos.
For any the -groupoid coincides with the fundamental ∞-groupoid of a locally ∞-connected (∞,1)-topos (see there) of the over-(∞,1)-topos .
In the cohesive (∞,1)-topos Top the intrinsic fundamental -groupoid functor coincides with the ordinary fundamental ∞-groupoid of a topological space. See discrete ∞-groupoid for details.
In ETop∞Grpd the intrinsic fundamental -groupoid is the generalization of that on Top to ∞-groupoids in paracompact spaces.