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Higher Topos Theory by Jacob Lurie
 
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Ebooks May 27, 2022 2

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Author
Jacob Lurie
Publisher
Princeton University Press 2009
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.
Higher Algebra by Jacob Lurie
 
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Ebooks May 27, 2022 2

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Author
Jacob Lurie
Publisher
Harvard University 2017
Contents: Stable infinite-Categories; infinite-Operads; Algebras and Modules over infinte-Operads; Associative Algebras and Their Modules;
Introduction to Categories and Categorical Logic by Samson Abramsky, Nikos Tzevelekos
 
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Ebooks May 25, 2022 2

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Author
Samson Abramsky, Nikos Tzevelekos
Publisher
arXiv 2011
The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The main prerequisite is a basic familiarity with the elements of discrete mathematics: sets, relations and functions.
Category Theory Lecture Notes by Daniele Turi
 
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Ebooks May 24, 2022 3

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Author
Daniele Turi
Publisher
University of Edinburgh 2001
These notes were written for an eighteen lectures 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.
Model Categories and Simplicial Methods by Paul Goerss, Kristen Schemmerhorn
 
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Ebooks May 24, 2022 3

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Author
Paul Goerss, Kristen Schemmerhorn
Publisher
Northwestern University 2004
There are many ways to present model categories, each with a different point of view. Here we'd like to treat model categories as a way to build and control resolutions. We're going to emphasize the analog of projective resolutions, simply because these are the sort of resolutions most people...
Category Theory Lecture Notes by Michael Barr, Charles Wells
 
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Ebooks May 23, 2022 3

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Author
Michael Barr, Charles Wells
Publisher
1999
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.
Category Theory
 
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Ebooks May 23, 2022 2

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Publisher
Wikibooks 2010
This Wikibook is an introduction to category theory. It is written for those who have some understanding of one or more branches of abstract mathematics, such as group theory, analysis or topology. The book contains many examples drawn from various branches of math.
Basic Category Theory by Jaap van Oosten
 
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Ebooks May 23, 2022 3

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Author
Jaap van Oosten
Publisher
University of Utrecht 2007
Contents: Categories and Functors; Natural transformations; (Co)cones and (Co)limits; A little piece of categorical logic; Adjunctions; Monads and Algebras; Cartesian closed categories and the lambda-calculus; Recursive Domain Equations.
Categories and Homological Algebra by Pierre Schapira
 
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Ebooks May 22, 2022 3

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Author
Pierre Schapira
Publisher
UPMC 2011
The aim of these notes is to introduce the reader to the language of categories and to present the basic notions of homological algebra, first from an elementary point of view, with the notion of derived functors, next with a more sophisticated approach, with the introduction of triangulated and...
Abelian Categories: an Introduction to the Theory of Functors by Peter Freyd
 
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Ebooks May 20, 2022 4

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Author
Peter Freyd
Publisher
Harper and Row 1964
From the table of contents: Fundamentals (Contravariant functors and dual categories); Fundamentals of Abelian categories; Special functors and subcategories; Metatheorems; Functor categories; Injective envelopes; Embedding theorems.
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