These properties concern the domain, the codomain and the image of functions.
These properties concern how the function is affected by arithmetic operations on its argument.
These notions extend directly to lambda calculus and type theory, respectively.
Examples are: Category theory is a branch of mathematics that formalizes the notion of a special function via arrows or morphisms.
dependently typed) binary operation called composition is provided on morphisms, every object has one special morphism from it to itself called the identity on that object, and composition and identities are required to obey certain relations.
Many common notions from mathematics (e.g. surjective, injective, free object, basis, finite representation, isomorphism) are definable purely in category theoretic terms (cf.