Functor

• Container with somewhere to store values(s)
• Some way of applying a function to values(s)
• Must return values(s) in same context

or a shorter explain:

a functor is simply something that can be mapped over

Monid

a monoid is a semigroup with an identity element.

Semigroup

A semigroup is an algebraic structure with a binary operation that satisfies the associativity law.

In PureScript, the binary operation for a semigroup that satisfies the associative property is called append, whose infix operator is <>

monoid

Identity: whenever we append one or more elements to it, we get back those elements

In PureScript, mempty (monoid empty) to reference the identity element of a monoid.