Mathematics Books Category Theory Books

Category Theory for Program Construction by Calculation (PDF 122P)

Category Theory for Program Construction by Calculation (PDF 122P)

Category Theory for Program Construction by Calculation (PDF 122P)

This note covers the following topics related to Category Theory: Notation, Basic Definitions, Sum and Product, Adjunctions, Cartesian Closed Categories, Algebras and Monads.

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s122 Pages
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Category Theory Lecture Notes by McGill University

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.

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Introduction To Category Theory And Categorical Logic

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.

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Category Theory A Programming Language Oriented Introduction

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.

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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.

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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.

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Category Theory for Program Construction by Calculation (PDF 122P)

Category Theory for Program Construction by Calculation (PDF 122P)

This note covers the following topics related to Category Theory: Notation, Basic Definitions, Sum and Product, Adjunctions, Cartesian Closed Categories, Algebras and Monads.

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Category Theory Lecture Notes (PDF 61P)

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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.

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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.

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Basic     Category Theory (PDF 88p)

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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.

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