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 Jacob Lurie - Harvard University
Contents: Stable infinite-Categories; infinite-Operads; Algebras and Modules over infinte-Operads; Associative Algebras and Their Modules; Little Cubes and Factorizable Sheaves; Algebraic Structures on infinite-Categories; and more.
by Peter Smith - Logic Matters
I hope that what is here may prove useful to others starting to get to grips with category theory. This text is intended to be relatively accessible; in particular, it presupposes rather less mathematical background than some texts on categories.
by Michael Barr, Charles Wells - Springer-Verlag
Introduction to toposes, triples and theories and the connections between them. The book starts with an introduction to category theory, then introduces each of the three topics of the title. Exercises provide examples or develop the theory further.
by 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.