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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 
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
Parametrized higher category theory
This book contains below topics, Cocartesian fibrations and model categories of marked simplicial sets, Functor categories, Join and slice, Limits and colimits, Assembling Sslice categories from ordinary slice categories, Types of Sfibrations, Relative adjunctions, Parametrized colimits, Kan extensions, Yoneda lemma, Bousfield Kan formula, fibrant replacement.
Author(s): Jay Shah
83 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 A Programming Language Oriented Introduction
This book explains the following topics, Categories, functors, natural transformations, String diagrams, Kan extensions, Algebras, coalgebras, bialgebras, Lambdacalculus 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