In programming, a functor is a structure with “elements” which you can apply a function to. The idea is that the type of elements is a parameter, called A, say

In programming, a functor is a structure with “elements” which you can apply a function to. The idea is that the type of elements is a parameter, called A, say. Then you use functorialty to change all the elements to something of a different type (or a different element of the same type). For instance List(A) is the type of lists of elements of type A. If you have a function f taking input A and giving output of type B you can “apply the functorial action” of List to transform a List(A) to List(B). For lists “the functorial action is simply mapping the function on each element. But being able to abstract over all functors can give very general implementations of interesting algorithms and patterns which then applies to many situations.