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Higher Dimensional Categories an illustrated guide book
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
182 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
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
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
263 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
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
393 Pages
Category Theory Lecture Notes for ESSLLI (PDF 133P)
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
133 Pages
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Author(s): NA
NA Pages
Category Theory Lecture Notes (PDF 61P)
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
61 Pages
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
Basic Category Theory (PDF 88p)
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
88 PagesAdvertisement
