The study of structure-preserving maps between mathematical objects, expressed through objects, arrows (morphisms), and functors.
A category consists of objects and composable morphisms satisfying identity and associativity
functors map between categories, preserving composition and identity
natural transformations map between functors, forming morphisms of morphisms
isomorphism identifies structurally identical objects regardless of representation
adjunctions capture universal construction patterns across mathematics
The Yoneda lemma states that an object is fully determined by its relationships to all other objects
Unifying language for set theory, algebra, topology, logic, and type theory
Related:: graph theory, linear algebra, information theory