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Category Theory Books

Category Theory Books

There are many online resources where you can find free Category Theory books to download in PDF format, including online textbooks, ebooks, lecture notes, and more, covering basic, beginner, and advanced concepts for those looking for an introduction to the subject or a deeper understanding of it.

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):

s 133Pages

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.

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s 258Pages

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):

s 292Pages

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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s 117Pages

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):

s 145Pages

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.

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s 90Pages

Computational Category Theory

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.

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s 263Pages

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.

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s NAPages

Lecture NotesCategory Theory

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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s NAPages

Tensor Categorie (PDF 93P)

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):

s 393Pages

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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s 122Pages

Notes on Category Theory (PDF 416P)

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):

s 416Pages

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):

s 133Pages

Brief notes on category theory (PDF 36P)

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.

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s 36Pages

Mixed Motives

Currently this section contains no detailed description for the page, will update this page soon.

Author(s):

s NAPages

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.

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s 61Pages

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):

s NAPages

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):

s 88Pages