• Corpus ID: 5338947

Higher Topos Theory

  title={Higher Topos Theory},
  author={Jacob Lurie},
  • J. Lurie
  • Published 2 August 2006
  • Philosophy, Mathematics
This purpose of this book is twofold: to provide a general introduction to higher category theory (using the formalism of "quasicategories" or "weak Kan complexes"), and to apply this theory to the study of higher versions of Grothendieck topoi. A few applications to classical topology are included. 
Yoneda's lemma for internal higher categories
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A theory of elementary higher toposes
We define an elementary higher topos that simultaneously generalizes an elementary topos and higher topos. Then we show it satisfies classical topos theoretic properties, such being locally Cartesian
Quillen model categories
We provide a brief description of the mathematics that led to Daniel Quillen’s introduction of model categories, a summary of his seminal work “Homotopical algebra”, and a brief description of some
Transfinite limits in topos theory
For a coherent site we construct a canonically associated enlarged coherent site, such that cohomology of bounded below complexes is preserved by the enlargement. In the topos associated to the
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Cech and Steenrod Homotopy Theories with Applications to Geometric Topology
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On quasi-categories as a foundation for higher algebraic stacks
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Simplicial Homotopy Theory
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