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Introduction to Category Theory
This note teaches the basics of category theory, in a way that is accessible and relevant to computer scientists. The emphasis is on gaining a good understanding the basic definitions, examples, and techniques, so that students are equipped for further study on their own of more advanced topics if required.
Author(s): Graham Hutton, School of Computer Science, University of Nottingham
NA Pages 
This book contains below topics, Note to the reader, Categories functors and natural transformations, Adjoints, Interlude on sets, Representables, Limits, Adjoints representables and limits, Index of notation.
Author(s): Tom Leinster
191 Pages
As categorical dimension increases, constructions such as cylinders, cones, and suspensions are no longer functorial in the old sense. These notes extend higher categories to oriented and antioriented categories. Compositions there commute only up to a coherent interchange law.
Author(s): David Gepner, Hadrian Heine
67 Pages
This paper looks at diagrammatic category and keeps the language simple. It asks what diagrammatic is, how category fits, and what a student should notice. Count, size, and order in diagrammatic are compared with everyday numbers.
Author(s): Kenji Nakahira
99 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 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
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, 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 and nbsp, 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
This note covers the following topics, and nbsp, Monoidal categories, The pentagon axiom, Basic properties of unit objects in monoidal categories, monoidal categories, Monoidal functors, equivalence of monoidal categories, Morphisms of monoidal functors, MacLanes strictness theorem, The MacLane coherence theorem, Invertible objects, Exactness of the tensor product, Semisimplicity of the unit object, Groupoids, Finite abelian categories and exact faithful functors, Fiber functors, Hopf algebras, Pointed tensor categories and pointed Hopf algebras, Chevalleys theorem, The AndruskiewitschSchneider conjecture, The CartierKostant theorem, Pivotal categories and dimensions, Spherical categories and Grothendieck rings of semisimple tensor categories.
Author(s): P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik
393 Pages