Category Theory
Overview
The study of mathematical structures and their relations via arrows (morphisms). Eilenberg–Mac Lane (1940s) introduced categories; Grothendieck applied them to algebraic geometry.
Era: 1940s–
Proposed at: New York, USA / Paris, France
Formal structure
Domain: Category C; objects X, Y; morphisms f: X → Y; functors F: C → D
F(id) = id; F(g ∘ f) = F(g) ∘ F(f); natural transformation η: F ⇒ G
Constraints: Composition associative; identity laws; Yoneda: Hom(Hom(-,A), F) ≃ F(A)
Objective: Abstract and unify mathematical structures