The definition of a monoid is wholly equivalent to that of a single-object category.
Given a monoid π=(π,β), one may construct a category ππ
consisting of a single object β
such that ππ(β,β)=π and composition is given by (β).
Conversely, π’(β,β) forms a monoid under composition for any ββObβ‘π’.
Thus a category is the oidification of a monoid, i.e. a monoidoid.