# The composition of morphisms in a monoidal category corresponds to an associative binary operation¶

For a monoidal category $M$ each morphism in $M(m, m)$ corresponds to the operation defined for the associated monoidal set on one of the elements.

For example, in the set of natural numbers $\mathbb{N}$ there will be a morphism corresponding to each partially-applied operation ${+0, +1, ..., +n}$.

Composing any two of these morphisms corresponds to performing the operation - the operation is associative because composition of morphisms is associative.