Mathematics – Category Theory
Scientific paper
2003-06-05
Mathematics
Category Theory
60 pages
Scientific paper
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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