Functors

Note to self

A Functor is a design pattern that evolves from category theory in mathematics. Fundamentally it’s a mapping between categories that preserves the structure of the original categories involved. It satisfies two laws: -

1. Identity law: $\small{F(\operatorname{id}_A) = \operatorname{id}_{F(A)}}$
2. Composition law: $\small{F(g \circ f) = F(g) \circ F(f)}$

Reading list

• Category Theory
• Covariance and Contravariance
• Java Functors