Adjunctions: Pairs of Adjoint Functors
A detailed guide to adjunctions: pairs of adjoint functors. Covers key methods, mathematical significance, and real-world applications.
Category Theory
20 articles
Cartesian Closed Categories and Exponential Objects
A detailed guide to cartesian closed categories and exponential objects. Covers key methods, mathematical significance, and real-world applications.
Categories: Objects, Morphisms, and Composition
A detailed guide to categories: objects, morphisms, and composition. Covers key methods, mathematical significance, and real-world applications.
Category Theory in Logic: Categorical Logic
A detailed guide to category theory in logic: categorical logic. Covers key methods, mathematical significance, and real-world applications.
Category Theory in Physics: Quantum Foundations
A detailed guide to category theory in physics: quantum foundations. Covers key methods, mathematical significance, and real-world applications.
Category Theory in Programming: Functional Programming
A detailed guide to category theory in programming: functional programming. Covers key methods, mathematical significance, and real-world applications.
Comonads and Their Applications
A detailed guide to comonads and their applications. Covers key methods, mathematical significance, and real-world applications.
Enriched Category Theory: Categories with Extra Structure
A detailed guide to enriched category theory: categories with extra structure. Covers key methods, mathematical significance, and real-world applications.
Equalizers and Coequalizers
A detailed guide to equalizers and coequalizers. Covers key methods, mathematical significance, and real-world applications.
Functors: Structure-Preserving Maps Between Categories
A detailed guide to functors: structure-preserving maps between categories. Covers key methods, mathematical significance, and real-world applications.
Higher Category Theory: 2-Categories and Beyond
A detailed guide to higher category theory: 2-categories and beyond. Covers key methods, mathematical significance, and real-world applications.
Limits and Colimits: General Framework
A detailed guide to limits and colimits: general framework. Covers key methods, mathematical significance, and real-world applications.
Monads: Algebras and Kleisli Categories
A detailed guide to monads: algebras and kleisli categories. Covers key methods, mathematical significance, and real-world applications.
Monoidal Categories and String Diagrams
A detailed guide to monoidal categories and string diagrams. Covers key methods, mathematical significance, and real-world applications.
Natural Transformations: Comparing Functors
A detailed guide to natural transformations: comparing functors. Covers key methods, mathematical significance, and real-world applications.
Products and Coproducts: Universal Constructions
A detailed guide to products and coproducts: universal constructions. Covers key methods, mathematical significance, and real-world applications.
Pullbacks and Pushouts: Limits and Colimits
A detailed guide to pullbacks and pushouts: limits and colimits. Covers key methods, mathematical significance, and real-world applications.
Topos Theory: Generalized Set Theories
A detailed guide to topos theory: generalized set theories. Covers key methods, mathematical significance, and real-world applications.
Universal Properties: Initial and Terminal Objects
A detailed guide to universal properties: initial and terminal objects. Covers key methods, mathematical significance, and real-world applications.
Yoneda Lemma: Representing Functors
A detailed guide to yoneda lemma: representing functors. Covers key methods, mathematical significance, and real-world applications.