Given a category$C$ and objects $a, b \in Ob(A)$, a pair of morphisms$f, g \in Mor(a, b)$ are jointly monic if for every object $c:Ob(A)$ and pair of morphisms $h, k \in Mor(c, a)$, $f \circ h = f \circ k$ and $g \circ h = g \circ k$ imply that $h = k$.

In a well-pointed category$C$, given objects $a, b \in Ob(A)$, a pair of morphisms$f, g \in Mor(a, b)$ are jointly injective if for every global element$h, k \in Mor(1, a)$, $f \circ h = f \circ k$ and $g \circ h = g \circ k$ imply that $h = k$.

In tablular allegories

In every tabular allegory, a relation $R$ could be factored into jointly monic maps$f$ and $g$ such that $f^\dagger \circ g = R$.