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Category Theory Lecture Notes by McGill University
This note covers the following topics: Preliminaries, Categories, Properties of objects and arrows, Functors, Diagrams and naturality, Products and sums, Cartesian closed categories, Limits and colimits, Adjoints, Triples, Toposes and Categories with monoidal structure.
Author(s): Department of Mathematics and Statistics,McGill University
133 Pages 
An introduction to Category Theory by Valdis Laan
This note explains categories, Properties of morphisms and objects, Functors, Natural transformations, Limits and colimits, Adjunctions.
Author(s): Valdis Laan
52 Pages
Category Theory in Context by Emily Riehl
This PDF book covers the following topics related to Category Theory : Categories, Functors, Natural Transformations, Universal Properties, Representability, and the Yoneda Lemma, Limits and Colimits, Adjunctions, Monads and their Algebras, All Concepts are Kan Extensions.
Author(s): Emily Riehl
258 Pages
Categorical homotopy theory by Emily Riehl
This PDF book covers the following topics related to Category Theory : All concepts are Kan extensions, Derived functors via deformations, Basic concepts of enriched category theory, The unreasonably effective bar construction, Homotopy limits and colimits: the practice, Weighted limits and colimits, Categorical tools for homotopy limit computations, Weighted homotopy limits and colimits, Derived enrichment, Weak factorization systems in model categories, Algebraic perspectives on the small object argument, Enriched factorizations and enriched lifting properties, A brief tour of Reedy category theory,. Preliminaries on quasi-categories, Simplicial categories and homotopy coherence, Isomorphisms in quasi-categories, A sampling of 2-categorical aspects of quasi-category theory.
Author(s): Emily Riehl
292 Pages
Introduction To Category Theory And Categorical Logic
This note covers the following topics related to Category Theory: Categories, Functors and Natural Transformations, subcategories, Full and Faithful Functors, Equivalences, Comma Categories and Slice Categories, Yoneda Lemma, Grothendieck universes, Limits and Colimits, Adjoint Functors, Adjoint Functor Theorems, Monads, Elementary Toposes, Cartesian Closed Categories, Logic of Toposes and Sheaves.
Author(s): Thomas Streicher
117 Pages
Category Theory A Programming Language Oriented Introduction
This book explains the following topics: Categories, functors, natural transformations, String diagrams, Kan extensions, Algebras, coalgebras, bialgebras, Lambda-calculus and categories.
Author(s): Pierre-Louis Curien
145 Pages
Category Theory by Prof. Dr. B. Pareigis
This book explains the following topics related to Category Theory:Foundations, Graphs, Monoids, Categories, Constructions on categories, Functors, Special types of functors, Natural transformations, Representable functors and the Yoneda Lemma, Terminal and initial objects, The extension principle, Isomorphisms, Monomorphisms and epimorphisms, Products, Adjoint functors and monads.
Author(s): Prof. Dr. B. Pareigis
90 Pages
Category Theory for Scientists
Purpose of this course note is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields.
Author(s): David I. Spivak
NA Pages
Category theory, a branch of abstract algebra, has found many applications in mathematics, logic, and computer science. Like such fields as elementary logic and set theory, category theory provides a basic conceptual apparatus and a collection of formal methods useful for addressing certain kinds of commonly occurring formal and informal problems, particularly those involving structural and functional considerations. This course note is intended to acquaint students with these methods, and also to encourage them to reflect on the interrelations between category theory and the other basic formal disciplines.
Author(s): Steve Awodey
NA Pages