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Mathematics  2003 

On Infinity Topoi

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In this paper we investigate an infinitely categorical analogue of the theory of Grothendieck topoi. In particular, we define infinity topoi and prove an analogue of Giraud's theorem, expressing the equivalence of ``intrinsic'' and ``extrinsic'' definitions. We also discuss the relationship between the theory of infinity topoi and classical topics in homotopy theory and dimension theory.


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