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  • lo. logic - What is a topos? - MathOverflow
    As Charley mentions, topoi have many nice properties, and since a topos is something which looks like sheaves of sets on a Grothendieck site, it should be clear why a topos theory would be useful In his book, Lurie develops, among other things, a theory of infinity-topoi, of which perhaps the main example of interest is sheaves of topological spaces on a Grothendieck site
  • Topos-theoretic Galois theory - MathOverflow
    So correct me if I'm wrong ) Is there more of "topos-theoretic Galois theory" in SGA 4 or are these the only two paragraphs about that topic? Concerning the definition of the fundamental group of a topos, there is a construction in Moerdijk's Classifying Spaces and Classifying Topoi, in which he nevertheless remarks:
  • Interview of Connes, Caramello, and L. Lafforgue about topos theory
    Around 45:30, the journalist claims that topos theory gets very bad press and asks why to Connes, Caramello and Lafforgue Connes says no, this is a completely external vision of reality Prompted by the journalist, he explains what is topos theory, where one studies a space not by looking at it directly, but by putting him behind the scenes
  • Major applications of the internal language of toposes
    applying Barr's theorem and passing to a Grothendieck topos that (is boolean and) satisfies the (external) axiom of choice (I mention homological algebra and homotopy theory here because, if I recall correctly, the former strategy was used – in the first instance – in the foundations of those topics, before the development of "direct" proofs )
  • Higher Topos Theory- whats the moral? - MathOverflow
    I've often seen Lurie's Higher Topos Theory praised as the next "great" mathematical book As someone who isn't particularly up-to-date on the state of modern homotopy theory, the book seems like a lot of abstract nonsense and the initial developments unmotivated
  • If I want to study Jacob Luries books Higher Topoi Theory, Derived . . .
    To read Higher Topos Theory, you'll need familiarity with ordinary category theory and with the homotopy theory of simplicial sets (Peter May's book "Simplicial Objects in Algebraic Topology" is a good place to learn the latter) Other topics (such as classical topos theory) will be helpful for motivation
  • What are Jacob Luries key insights? - MathOverflow
    People had looked at $\infty$-categories for years, and the idea of $(\infty,n)$-categories is not in itself new What was the key new idea which started "Higher Topos Theory", the proof of the Baez-Dolan cobordism hypothesis, "Derived Algebraic Geometry", etc ?
  • topos theory - Stone Spaces, Locales, and Topoi for the (relative . . .
    My first "Topos Theory" book was Johnstone (some title), was hard but page after page I assimilated this (I'm still alive more or less), but it was the only book in argument For me opinion the Borceaux's third volume is very good I indicate these text in progressive difficulty and depth : S Mac Lane, I Moerdijk, Sheaves in Geometry and Logic


















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