Higher Topos Theory
by Jacob Lurie
Publisher: Princeton University Press 2009
ISBN/ASIN: 0691140499
ISBN-13: 9780691140490
Number of pages: 943
Description:
Jacob Lurie presents the foundations of higher category 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.
Download or read it online for free here:
Download link
(3.9MB, PDF)
Similar books
Notes on Categories and Groupoidsby P. J. Higgins - Van Nostrand Reinhold
A self-contained account of the elementary theory of groupoids and some of its uses in group theory and topology. Category theory appears as a secondary topic whenever it is relevant to the main issue, and its treatment is by no means systematic.
(13386 views)
Combinatorics and Algebra of Tensor Calculusby Sen Hu, Xuexing Lu, Yu Ye - arXiv
In this paper, we reveal the combinatorial nature of tensor calculus for strict tensor categories and show that there exists a monad which is described by the coarse-graining of graphs and characterizes the algebraic nature of tensor calculus.
(5203 views)
Seven Sketches in Compositionality: An Invitation to Applied Category Theoryby Brendan Fong, David I Spivak - arXiv.org
This book is an invitation to discover advanced topics in category theory through concrete, real-world examples. The tour takes place over seven sketches, such as databases, electric circuits, etc, with the exploration of a categorical structure.
(4568 views)
Category Theory Lecture Notesby Michael Barr, Charles Wells
Categories originally arose in mathematics out of the need of a formalism to describe the passage from one type of mathematical structure to another. These notes form a short summary of some major topics in category theory.
(10486 views)