Monoids

Monoid is a concept that comes from mathematics. We will take a look at it in more detail with all the theory needed to understand it later in this book. For now, it will be enough to remember that a monoid is an algebraic structure with a single associative binary operation and an identity element. Here are the keywords that you should remember:

• The associative binary operation. This means (a+b)+c = a+(b+c).
• The identity element. This means a+i = i+a = a. Here, the identity is i.

What is important about monoids is that they give us the possibility to work with many different types of values in a common way. They allow us to convert pairwise operations to work with sequences; the associativity gives us the possibility for parallelization, and the identity element allows us to know what to do with empty lists. Monoids are great to easily describe and implement aggregations.