category theory
E508538
Category theory is a branch of mathematics that studies abstract structures and relationships between them using the language of objects and morphisms, providing a unifying framework across many areas of math and theoretical computer science.
All labels observed (1)
| Label | Occurrences |
|---|---|
| category theory canonical | 4 |
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
branch of mathematics
ⓘ
mathematical theory ⓘ |
| aimsTo | express mathematical concepts via universal properties ⓘ |
| appliesTo |
algebra
ⓘ
logic ⓘ theoretical computer science ⓘ topology ⓘ |
| author | Saunders Mac Lane NERFINISHED ⓘ |
| characterizedBy | diagrammatic reasoning ⓘ |
| emphasizes | morphisms over elements ⓘ |
| fieldOfStudy |
mathematics
ⓘ
theoretical computer science ⓘ |
| focusesOn |
abstract structures
ⓘ
relationships between structures ⓘ |
| formalism | objects and morphisms ⓘ |
| hasKeyText | Categories for the Working Mathematician NERFINISHED ⓘ |
| hasSubfield |
enriched category theory
ⓘ
higher category theory ⓘ homological algebra ⓘ topos theory ⓘ |
| introducedBy |
Samuel Eilenberg
NERFINISHED
ⓘ
Saunders Mac Lane NERFINISHED ⓘ |
| introducedIn | 1940s ⓘ |
| notableConcept |
adjoint functor
ⓘ
category ⓘ colimit ⓘ commutative diagram ⓘ functor ⓘ initial object ⓘ limit ⓘ monad ⓘ natural transformation ⓘ terminal object ⓘ universal property ⓘ |
| provides | unifying framework for mathematics ⓘ |
| relatedTo |
model theory
ⓘ
set theory ⓘ universal algebra ⓘ |
| studies |
categories
ⓘ
functors ⓘ morphisms ⓘ natural transformations ⓘ objects ⓘ |
| usedIn |
algebraic geometry
ⓘ
functional programming ⓘ homotopy theory ⓘ semantics of programming languages ⓘ type theory ⓘ |
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Saunders Mac Lane