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A topos is a category that behaves very much like the category of sets and possesses a good notion of localization. Related to topos are: sheaves, presheaves, descent, stacks, localization,...

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What is the logical progression in algebraic tools for studying spaces (varieties -> schemes...

Some algebraists (Cartier, Weil, Atiyah, etc.) sometimes speak of geometry as a long history of essentially asking the same question—"what is space, and how would one describe a space uniquely". Histo …