Category Theory

Welcome to the Category Theory International Project !

Subject classification: this is a mathematics resource.

Subject classification: this is an information technology resource.

Educational level: this is a tertiary (university) resource.

• "In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them. Categories now appear in most branches of mathematics and in some areas of theoretical computer science and mathematical physics, and have been a unifying notion. Categories were first introduced by Samuel Eilenberg and Saunders Mac Lane in 1942-1945, in connection with algebraic topology."

• This is an International Project on Category Theory, Higher Dimensional Algebra and their Novel Applications, such as:

• Topoi,
• n-Categories
• Nonabelian Algebraic Topology,

Applications and Applied Mathematics

• Categorical Dynamics,
• Computational Theory and Logic,
• Quantum Physics and Quantum Algebraic Topology,
• Complex Systems and Relational Biology,
  • Mathematical Medicine
  • Ecosystems
  • Biosphere
• Sociology
• Categorical Ontology
• Philosophy of Science
• (Specify your own novel application field, such as Anabelian Geometry, Noncommutative Geometry, Nondistributive Logics, Monassociative Mathematics, NonNewtonian analysis, etc)

w:Category theory topics w:Homological algebra: w:Abelian category • w:Sheaf theory • w:K-theory

w:Topos theory • w:Enriched category theory • w:Higher category theory

  w:Monoidal category • w:Closed category • w:Dagger category

More category theory topics

Categorical diagram of a pushout

External links

• The n-Category Café
  • At “Geometry, Quantum Fields, and Strings: Categorial Aspects”,Posted by Urs Schreiber
  • nonabelian cohomology
  • Nonabelian Cohomology in Three (∞,1)-Toposes

Things to do

• Improve the category theory articles, expand the category theory stubs
• Keep building this entry

List of Participants

1. 1
2. 2 User:Bci21
3. 3

. . .

1. N

Resources

• Introduction to Category Theory
• Category Theory Wikibook

• "Abelian Categories" (fr) by Pierre Gabriel
• Grothendieck, Alexander. Éléments de géométrie algébrique (rédigés avec la collaboration de Jean Dieudonné) : I. Le langage des schémas. Publications Mathématiques de l'IHÉS, 4 (1960), p. 5-228
• Des Catégories Abéliennes-Bulletin de la Société Mathématique de France, 90 (1962), p. 323-448