Download e-book for kindle: Higher Topos Theory (AM-170) (Annals of Mathematics Studies) by Jacob Lurie

Higher type concept is mostly considered as technical and forbidding, yet a part of it really is significantly extra tractable: the idea of infinity-categories, greater different types within which all greater morphisms are assumed to be invertible. In Higher Topos Theory, Jacob Lurie provides the principles of this thought, utilizing the language of susceptible Kan complexes brought by way of Boardman and Vogt, and indicates how present theorems in algebraic topology might be reformulated and generalized within the theory's new language. the result's a strong idea with functions in lots of parts of mathematics.

The book's first 5 chapters provide an exposition of the idea of infinity-categories that emphasizes their position as a generalization of standard different types. some of the primary principles from classical class concept are generalized to the infinity-categorical surroundings, corresponding to limits and colimits, adjoint functors, ind-objects and pro-objects, in the neighborhood available and presentable different types, Grothendieck fibrations, presheaves, and Yoneda's lemma. A 6th bankruptcy offers an infinity-categorical model of the speculation of Grothendieck topoi, introducing the inspiration of an infinity-topos, an infinity-category that resembles the infinity-category of topological areas within the feel that it satisfies sure axioms that codify a number of the uncomplicated rules of algebraic topology. A 7th and ultimate bankruptcy offers functions that illustrate connections among the idea of upper topoi and concepts from classical topology.