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When we abstract the notion of space, we get more and more isomorphisms. For example, the triangle, square and circle are not isometrical, but they are homeomorphic. If we take one step further to the sheaf toposes, do we get an isomorphism with another topos not defined as a sheaf topos? To the etale topos of a scheme maybe?

V. Semeria
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    No. The property of being a sheaf topos – even the property of being the sheaf topos of the circle – is invariant under equivalence. – Zhen Lin Apr 21 '23 at 22:25

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