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@hallasurvivor OK, thank you!

@hallasurvivor I'd love to read that MO discussion. Can you share the title, or the link? In this picture, what role plays the concept of topos? Recently I listened to an old talk by Colin McLarty about Grothendieck. Something that really got stuck in my head was the idea that topoi are the real right notion of space from Grothendieck pov... and that the topoi Grothendieck thinks of are not really the big categories satisfying the Giraud axioms but some kind of "ghosts" (my term) that manifest as the big categories that we know... he goes on explaining this by interpreting the product of two topoi (as categories) as somehow the avatar (my term) of the union of their underlying true topoi.