Concept
A language centred on objects, morphisms, and composition, used to compare recurring structures across mathematical fields.
Understand it in one breath
"Find the same relational structure across different fields." Groups with homomorphisms, topological spaces with continuous maps, and sets with functions can all be viewed as objects plus composable arrows. A functor preserves identities and composition, letting us compare structures between categories. Haskell's Functor and Monad type classes are inspired by these ideas rather than literal implementations of all their mathematics.
At a glance
Key formula
Modern applications
Functional programming in Haskell and Scala, the GHC compiler, and database-schema transformations.
Beyond MathVoyage
Loading…