๐Monoid
In Category Theory, Monoid is a Category with one object.
\begin{tikzcd} m \arrow[loop, "f", distance=2em, leftarrow, swap] \arrow[loop, "g", distance=4em, leftarrow, swap] \arrow[loop, "g \circ f", distance=6em, leftarrow, swap] \end{tikzcd}
In Set Theory, Monoid is a set of values with
an associative binary operator
a unit value
These definitions are equivalent.
set of values โ set of morphisms
associative binary operator โ composition of morphisms
unit value โ identity morphism