Lurie, Jacob 1977Overview
Most widely held works about
Jacob Lurie
Most widely held works by
Jacob Lurie
Higher topos theory
by Jacob Lurie
(
)
14 editions published in 2009 in English and held by 1,222 WorldCat member libraries worldwide Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinitycategories, higher categories in which all higher morphisms are assumed to be invertible. In Higher Topos Theory, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. The result is a powerful theory with applications in many areas of mathematics. The book's firs
Higher Topos Theory (AM170)
by Jacob Lurie
(
)
1 edition published in 2009 in English and held by 12 WorldCat member libraries worldwide Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinitycategories, higher categories in which all higher morphisms are assumed to be invertible. In Higher Topos Theory, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. The result is a powerful theory with applications in many areas of mathematics. The book's first five chapters give an exposition of the theory of infinitycategories that emphasizes their role as a generalization of ordinary categories. Many of the fundamental ideas from classical category theory are generalized to the infinitycategorical setting, such as limits and colimits, adjoint functors, indobjects and proobjects, locally accessible and presentable categories, Grothendieck fibrations, presheaves, and Yoneda's lemma. A sixth chapter presents an infinitycategorical version of the theory of Grothendieck topoi, introducing the notion of an infinitytopos, an infinitycategory that resembles the infinitycategory of topological spaces in the sense that it satisfies certain axioms that codify some of the basic principles of algebraic topology. A seventh and final chapter presents applications that illustrate connections between the theory of higher topoi and ideas from classical topology
On simply laced lie algebras and their minuscule representations
by Jacob Lurie
(
Book
)
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
Derived algebraic geometry
by Jacob Lurie
(
Book
)
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide The purpose of this document is to establish the foundations for a theory of derived algebraic geometry based upon simplicial commutative rings. We define derived versions of schemes, algebraic spaces, and algebraic stacks. Our main result is a derived analogue of Artin's representability theorem, which provides a precise criteria for the representability of a moduli functor by geometric objects of these types Audience Level
Related Identities
Associated Subjects

Alternative Names
Lurie, J. 1977
Languages
Covers
