Mathematics Books Category Theory Books

Computational Category Theory

Computational Category Theory

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.

Author(s):

s263 Pages
Similar Books
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.

s133 Pages
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.

s258 Pages
Computational Category Theory

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.

s263 Pages
Category Theory for Scientists

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.

sNA Pages
Lecture NotesCategory Theory

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.

sNA Pages
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.

s393 Pages
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.

s416 Pages
Category Theory Lecture Notes for ESSLLI (PDF 133P)

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.

s133 Pages
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.

s36 Pages
Mixed Motives

Mixed Motives

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

sNA Pages
Category Theory Lecture Notes (PDF 61P)

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.

s61 Pages

Advertisement