separated geometric morphism
Cohomology and homotopy
In higher category theory
A geometric morphism of toposes is separated if the diagonal is a proper geometric morphism.
In particular if is the terminal object in Topos, hence the canonical base topos Set, we say that a topos is a Hausdorff topos if is a proper geometric morphism.
More generally, since there is a hierarchy of notions of proper geometric morphism, there is accordingly a hierarchy of separatedness conditions.
In (Johnstone) this is example C3.2.24
Chapter II of
- Ieke Moerdijk, Jacob Vermeulen, Relative compactness conditions for toposes (pdf) and Proper maps of toposes , American Mathematical Society (2000)
Around def. C3.2.12 of
Revised on May 9, 2012 03:54:31
by Zoran Škoda