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.

Author(s):

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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Category Theory in Context by Emily Riehl

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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Categorical homotopy theory by Emily Riehl

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.

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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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Computational Category Theory

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Tensor Categorie (PDF 93P)

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.

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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.

s122 Pages
Notes on Category Theory (PDF 416P)

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.

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Brief notes on category theory (PDF 36P)

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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Mixed Motives

Mixed Motives

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

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Basic     Category Theory (PDF 88p)

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.

s88 Pages

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