Cotopological Congruence

A Congruence in an Infinity Topos is a cotopological congruence if it is generated by a class of Surjections.

Note that this is only relevant in an Infinity Topos; there are no non-trivial Infinity-Connected Objects in n-topoi! (EG: every infinity connected and N-Truncated Object is Contractible).

References

• Left-Exact Localizations of $\infty$-Topoi II, (4.2.1)