A monoid is an algebraic data structure that has a binary operation (+, *, ++, etc), and an empty element (0, 1, [], etc). In terms of relationship to other algebraic data structure, it "inherits" the binary operation from its Semigroup buddy, which is a very nice data structure to represent non-empty containers (and statically enforce that property).

Julie Moronuki's blog has helped me greatly to understand it all: https://argumatronic.com/posts/2019-06-21-algebra-cheatsheet...