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.
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by Daniele Turi - University of Edinburgh
These notes were written for a course in category theory. The course was designed to be self-contained, drawing most of the examples from category theory itself. It was intended for post-graduate students in theoretical computer science.
This book is an introduction to category theory, written for those who have some understanding of one or more branches of abstract mathematics, such as group theory, analysis or topology. It contains examples drawn from various branches of math.
by Eugenia Cheng, Aaron Lauda - University of Sheffield
This work gives an explanatory introduction to various definitions of higher-dimensional category. The emphasis is on ideas rather than formalities; the aim is to shed light on the formalities by emphasizing the intuitions that lead there.
by D. I. Spivak, C. Vasilakopoulou, P. Schultz - arXiv
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as 'machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time.