A unital magmoid$Q$ is a magmoid where every object $a \in Ob(Q)$ has an identity morphism$id_a: a \to a$, such that for any morphism $f:a \to b$, $f \circ id_a = f$, and for any morphism $g:c \to a$, $id_a \circ g = g$.

A unital magmoid is invertible if for every pair of objects $a,b \in Ob(Q)$ and for every morphism $f:a \to b$, there exists an inverse morphism$g:b \to a$ such that $f \circ g = id_b$ and $g \circ f = id_a$.