Higher Topos Theory
by Jacob Lurie
Publisher: Princeton University Press 2009
Number of pages: 943
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.
Home page url
Download or read it online for free here:
by Paul Goerss, Kristen Schemmerhorn - Northwestern University
There are many ways to present model categories, each with a different point of view. Here we would like to treat model categories as a way to build and control resolutions. We are going to emphasize the analog of projective resolutions.
by David I. Spivak - The MIT Press
This book shows that category theory can be useful outside of mathematics as a flexible modeling language throughout the sciences. Written in an engaging and straightforward style, the book is rigorous but accessible to non-mathematicians.
by Maarten M. Fokkinga - University of Twente
These notes present the important notions from category theory. The intention is to provide a fairly good skill in manipulating with those concepts formally. This text introduces category theory in the calculational style of the proofs.
by Tom Leinster - arXiv
Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from topology, quantum algebra, mathematical physics, logic, and computer science.