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arXiv:math/0306109math.CT

On Infinity Topoi

Jacob Lurie

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Abstract

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.

arXiv comments
60 pages
Journal reference
DOI
Subjects
math.CTCategory Theory math.ATAlgebraic Topology

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  1. Physics, Topology, Logic and Computation: A Rosetta Stone (2009) [pdf] 1 comment

    • Lurie's "On Infinity Topoi"[0] preceded the book and is, I quote[1], > 50 pages of pure cake, beautifully and informally written. The book is 1000 pages long. There is some new cake there, but not 20 times as much. [0] https://arxiv.org/abs/math/0306109 [1]…

      torusticView on HNParent context

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