Higher Topos Theory (AM-170)
By Jacob Lurie
()
Currently unavailable
Currently unavailable
About this ebook
Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, 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 infinity-categories that emphasizes their role as a generalization of ordinary categories. Many of the fundamental ideas from classical category theory are generalized to the infinity-categorical setting, such as limits and colimits, adjoint functors, ind-objects and pro-objects, locally accessible and presentable categories, Grothendieck fibrations, presheaves, and Yoneda's lemma. A sixth chapter presents an infinity-categorical version of the theory of Grothendieck topoi, introducing the notion of an infinity-topos, an infinity-category that resembles the infinity-category 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.
Jacob Lurie
Jacob Lurie is associate professor of mathematics at Massachusetts Institute of Technology.
Related to Higher Topos Theory (AM-170)
Titles in the series (100)
Algebraic Theory of Numbers. (AM-1), Volume 1 Rating: 0 out of 5 stars0 ratingsExistence Theorems in Partial Differential Equations. (AM-23), Volume 23 Rating: 0 out of 5 stars0 ratingsAn Introduction to Linear Transformations in Hilbert Space. (AM-4), Volume 4 Rating: 0 out of 5 stars0 ratingsConvergence and Uniformity in Topology. (AM-2), Volume 2 Rating: 0 out of 5 stars0 ratingsTranscendental Numbers. (AM-16) Rating: 0 out of 5 stars0 ratingsTopological Methods in the Theory of Functions of a Complex Variable. (AM-15), Volume 15 Rating: 0 out of 5 stars0 ratingsMetric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8) Rating: 0 out of 5 stars0 ratingsThe Two-Valued Iterative Systems of Mathematical Logic. (AM-5), Volume 5 Rating: 0 out of 5 stars0 ratingsProbleme General de la Stabilite du Mouvement. (AM-17), Volume 17 Rating: 0 out of 5 stars0 ratingsMeromorphic Functions and Analytic Curves. (AM-12) Rating: 0 out of 5 stars0 ratingsIntroduction to Non-Linear Mechanics. (AM-11), Volume 11 Rating: 0 out of 5 stars0 ratingsThe Calculi of Lambda-Conversion (AM-6), Volume 6 Rating: 4 out of 5 stars4/5Degree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9 Rating: 0 out of 5 stars0 ratingsConsistency of the Continuum Hypothesis. (AM-3), Volume 3 Rating: 0 out of 5 stars0 ratingsIsoperimetric Inequalities in Mathematical Physics. (AM-27), Volume 27 Rating: 0 out of 5 stars0 ratingsCurvature and Betti Numbers. (AM-32), Volume 32 Rating: 0 out of 5 stars0 ratingsContributions to Fourier Analysis. (AM-25) Rating: 0 out of 5 stars0 ratingsFinite Dimensional Vector Spaces. (AM-7), Volume 7 Rating: 4 out of 5 stars4/5Topics in Topology. (AM-10), Volume 10 Rating: 0 out of 5 stars0 ratingsAn Essay Toward a Unified Theory of Special Functions. (AM-18), Volume 18 Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Nonlinear Oscillations (AM-29), Volume II Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Nonlinear Oscillations (AM-20), Volume I Rating: 0 out of 5 stars0 ratingsLectures on Differential Equations. (AM-14), Volume 14 Rating: 0 out of 5 stars0 ratingsA Theory of Cross-Spaces. (AM-26), Volume 26 Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Games (AM-39), Volume III Rating: 0 out of 5 stars0 ratingsFunctional Operators (AM-22), Volume 2: The Geometry of Orthogonal Spaces. (AM-22) Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Games (AM-28), Volume II Rating: 0 out of 5 stars0 ratingsFourier Transforms. (AM-19), Volume 19 Rating: 0 out of 5 stars0 ratingsFunctional Operators (AM-21), Volume 1: Measures and Integrals. (AM-21) Rating: 0 out of 5 stars0 ratingsMorse Theory. (AM-51), Volume 51 Rating: 4 out of 5 stars4/5
Related ebooks
Lectures on Homotopy Theory Rating: 0 out of 5 stars0 ratingsAlgebraic Equations: An Introduction to the Theories of Lagrange and Galois Rating: 4 out of 5 stars4/5Lectures on Modular Forms. (AM-48), Volume 48 Rating: 0 out of 5 stars0 ratingsRepresentation Theory of Finite Groups Rating: 4 out of 5 stars4/5Lectures on Modular Forms Rating: 0 out of 5 stars0 ratingsInfinite-Dimensional Topology: Prerequisites and Introduction Rating: 0 out of 5 stars0 ratingsAlgebra: Polynomials, Galois Theory and Applications Rating: 0 out of 5 stars0 ratingsMorse Theory. (AM-51), Volume 51 Rating: 4 out of 5 stars4/5Differential Forms in Algebraic Topology Rating: 5 out of 5 stars5/5Introduction to Lie Groups and Lie Algebra, 51 Rating: 0 out of 5 stars0 ratingsResiduation Theory Rating: 0 out of 5 stars0 ratingsAxiomatic Projective Geometry Rating: 2 out of 5 stars2/5Infinite Loop Spaces (AM-90), Volume 90: Hermann Weyl Lectures, The Institute for Advanced Study. (AM-90) Rating: 0 out of 5 stars0 ratingsIntroduction to Homological Algebra, 85 Rating: 4 out of 5 stars4/5An Introduction to Finite Projective Planes Rating: 0 out of 5 stars0 ratingsHomotopy Theory: An Introduction to Algebraic Topology Rating: 0 out of 5 stars0 ratingsGroups and Characters Rating: 0 out of 5 stars0 ratingsHilbert Spaces Rating: 0 out of 5 stars0 ratingsThe Ergodic Theory of Lattice Subgroups (AM-172) Rating: 0 out of 5 stars0 ratingsTopological Spaces Rating: 0 out of 5 stars0 ratingsElements of Analytical Dynamics Rating: 0 out of 5 stars0 ratingsVector Bundles - Vol 1: Foundations and Stiefel - Whitney Classes Rating: 5 out of 5 stars5/5Etale Homotopy of Simplicial Schemes. (AM-104), Volume 104 Rating: 1 out of 5 stars1/5The Topology of Fibre Bundles. (PMS-14), Volume 14 Rating: 5 out of 5 stars5/5The Classical Groups: Their Invariants and Representations (PMS-1) Rating: 4 out of 5 stars4/5An Introduction to Variational Inequalities and Their Applications Rating: 0 out of 5 stars0 ratingsComplexes and Manifolds: The Mathematical Works of J. H. C. Whitehead Rating: 5 out of 5 stars5/5Introductory Lectures on Equivariant Cohomology: (AMS-204) Rating: 0 out of 5 stars0 ratingsIntroduction to Group Theory with Applications: Materials Science and Technology Rating: 1 out of 5 stars1/5Harvey Friedman's Research on the Foundations of Mathematics Rating: 0 out of 5 stars0 ratings
Mathematics For You
Algebra - The Very Basics Rating: 5 out of 5 stars5/5Calculus Made Easy Rating: 4 out of 5 stars4/5Geometry For Dummies Rating: 5 out of 5 stars5/5Mental Math Secrets - How To Be a Human Calculator Rating: 5 out of 5 stars5/5The Everything Guide to Algebra: A Step-by-Step Guide to the Basics of Algebra - in Plain English! Rating: 4 out of 5 stars4/5Game Theory: A Simple Introduction Rating: 4 out of 5 stars4/5Quantum Physics for Beginners Rating: 4 out of 5 stars4/5Precalculus: A Self-Teaching Guide Rating: 5 out of 5 stars5/5Basic Math & Pre-Algebra For Dummies Rating: 4 out of 5 stars4/5Introducing Game Theory: A Graphic Guide Rating: 4 out of 5 stars4/5The Thirteen Books of the Elements, Vol. 1 Rating: 0 out of 5 stars0 ratingsThe Everything Everyday Math Book: From Tipping to Taxes, All the Real-World, Everyday Math Skills You Need Rating: 5 out of 5 stars5/5Algebra I Workbook For Dummies Rating: 3 out of 5 stars3/5The Little Book of Mathematical Principles, Theories & Things Rating: 3 out of 5 stars3/5Is God a Mathematician? Rating: 4 out of 5 stars4/5Real Estate by the Numbers: A Complete Reference Guide to Deal Analysis Rating: 0 out of 5 stars0 ratingsThe Golden Ratio: The Divine Beauty of Mathematics Rating: 5 out of 5 stars5/5Relativity: The special and the general theory Rating: 5 out of 5 stars5/5Algebra II For Dummies Rating: 3 out of 5 stars3/5Summary of The Black Swan: by Nassim Nicholas Taleb | Includes Analysis Rating: 5 out of 5 stars5/5See Ya Later Calculator: Simple Math Tricks You Can Do in Your Head Rating: 4 out of 5 stars4/5My Best Mathematical and Logic Puzzles Rating: 5 out of 5 stars5/5Sneaky Math: A Graphic Primer with Projects Rating: 0 out of 5 stars0 ratingsA Mind for Numbers | Summary Rating: 4 out of 5 stars4/5ACT Math & Science Prep: Includes 500+ Practice Questions Rating: 3 out of 5 stars3/5
Reviews for Higher Topos Theory (AM-170)
0 ratings0 reviews