Higher Algebra by Jacob Lurie
Higher Algebra - Table of Contents
1. Stable 8-Categories
2. 8-Operads
3. Algebras and Modules over 8-Operads
4. Associative Algebras and Their Modules
5. Little Cubes and Factorizable Sheaves
6. The Calculus of Functors
7. Algebra in the Stable Homotopy Category
A. Constructible Sheaves and Exit Paths
B. Categorical Patterns
What You Will Learn in Higher Algebra
"Higher Algebra" by "Jacob Lurie" is a highly advanced mathematics book that redefines algebra using modern ideas from higher category theory. Instead of focusing on classical algebra alone, the book develops algebraic structures within the framework of 8-categories, offering a deeper and more flexible foundation for modern mathematics.
The book extends familiar objects such as rings, modules, and monoidal categories into "higher categories", allowing mathematicians to study algebra in contexts where homotopy and higher-dimensional structures matter. Central themes include "derived algebra", "spectral algebra", and "homotopy theory", which are essential in current research in algebraic geometry and topology. The writing is rigorous and precise, intended for readers with strong mathematical backgrounds.
"Higher Algebra" is not a beginner’s text but a foundational reference for researchers and advanced graduate students. It has had a major impact on modern mathematics by shaping how "algebra", "infinity categories", "structures", "homotopy", and "theory" are understood and used in contemporary research.
Book Details & Specifications
Title:
Higher Algebra by Jacob Lurie
Publisher:
Harvard University
Year:
2017
Pages:
1553
Type:
PDF
Language:
English
ISBN-10 #:
1402179650
ISBN-13 #:
978-1402179655
License:
External Educational Resource
Amazon:
Amazon
About the Author: Jacob Lurie
The author
Jacob Lurie
(born 1977) is an American mathematician and professor at Department of Mathematics, Harvard University, Cambridge. He is known for transforming modern mathematics through deep and original ideas. He is a professor at the Institute for Advanced Study and works at the intersection of "algebra", "topology", and higher structures. Lurie is best known for "Higher Algebra", where he develops mathematics using "infinity categories" and "homotopy theory". His work underpins "derived algebraic geometry" and has had a major influence on contemporary research, shaping how advanced algebraic "structures" are understood today. He also received the Morgan Prize for his undergraduate thesis on Lie algebras.
Read or Downloadable Higher Algebra
Category Theory