The book is aimed primarily at the beginning graduate student.It gives the de nition of this notion, goes through the various associated gadgetry such as functors, natural transformations, limits and colimits, and then explains adjunctions.
Author(s): Harold Simmons
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
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
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
This book emphasizes category theory in conceptual aspects, so that category theory has come to be viewed as a theory whose purpose is to provide a certain kind of conceptual clarity.
Author(s): D.E. Rydeheard and R.M. Burstal
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
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
This note covers the following topics: 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, MacLane's 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, Chevalley's theorem, The Andruskiewitsch-Schneider conjecture, The Cartier-Kostant 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
This note covers the following topics related to Category Theory: Notation, Basic Definitions, Sum and Product, Adjunctions, Cartesian Closed Categories, Algebras and Monads.
Author(s): Lambert Meertens
These notes are targeted to a student with significant mathematical sophistication and a modest amount of specific knowledge. Covered topics are: Mathematics in Categories, Constructing Categories, Functors and Natural Transformations, Universal Mapping Properties, Algebraic Categories, Cartesian Closed Categories, Monoidal Categories, Enriched Category Theory, Additive and Abelian Categories, 2-Categories and Fibered Categories.
Author(s): Robert L. Knighten
This note covers the following topics related to Category Theory: Functional programming languages as categories, Mathematical structures as categories, Categories of sets with structure, Categories of algebraic structures, Constructions on categories, Properties of objects and arrows, Functors, Diagrams and naturality, Products and sums, Cartesian closed categories, Limits and colimits, Adjoints, Triples, Toposes, Categories with monoidal structure.
Author(s): Michael Barr and Charles Wells
This note explains the following topics related to Category Theory: Duality, Universal and couniversal properties, Limits and colimits, Biproducts in Vect and Rel, Functors, Natural transformations, Yoneda'a Lemma, Adjoint Functors, Cartesian Closed Categories, The Curry-Howard-Lambek Isomorphism, Induction and Coinduction, Stream programming examples and Monads.
Author(s): Prakash Panangaden
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Author(s): NA
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 emphasising the intuitions that lead there. Covered topics are: Penon, Batanin and Leinster, Opetopic, Tamsamani and Simpson, Trimble and May.
Author(s): Eugenia Cheng and Aaron Lauda
Higher dimensional category theory is the study of n categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from areas as diverse as topology, quantum algebra, mathematical physics, logic, and theoretical computer science. This is the first book on the subject and lays its foundations.
Author(s): Tom Leinster
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Author(s): NA
This note covers the following topics: Universal Problems, Basic Notions, Universality, Natural Transformations and Functor Categories, Colimits, Duality and LKan Extensions imits, Adjunctions, Preservation of Limits and Colimits, Monads, Lawvere Theories, Cartesian Closed Categories, Variable Sets and Yoneda Lemma and 2-Categories.
Author(s): Daniele Turi
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
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Author(s): NA
This note covers the following topics: Categories and Functors, Natural transformations, Examples of natural transformations, Equivalence of categories, cones and limits, Limits by products and equalizers, Colimits, A little piece of categorical logic, The logic of regular categories.
Author(s): Jaap van Oosten