It is well known that (Grothendieck) Topos (in fact, Model topos too) has many good geometrical properties. In many senses reflects general forms of generic geometry.

Note: Grothendieck view of Topos is as an "ultimate" generalization of space.

Also, Elementary topos has many good logical properties. I am interested in elementary topos as a formal geometry.

>**Question:** _Elementary topos can be seen as a generalized space?_

Note: The "Elementary higher topos" can reflects the geometrical nature of objects in mathematics? This could suggest the physical nature of mathematics (this is vague, only a philosophical note).