Composition

The act of combining the application of multiple Functions into one function.

• Age is a function that maps People to Integers
• GreaterThan18 is a function that maps Integers to Booleans
• GreaterThan18 $\circ$ Age is the Composition of the above functions that maps People to Booleans
  • It is equivalent to applying Age, then applying GreaterThan18
  • It can be thought of as: GreaterThan18 follows Age
  • GreaterThan18 $\circ$ Age = Age(GreaterThan18(…))
• id is the Identity Morphism, which is depicted above to map People to People
  • It exists for all sets, but is omitted for the others