nLab jointly monic morphisms

Definition

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 $f^\dagger \circ g = R$.

See also

• monomorphism

• internal relation

• regular category

• tabular allegory

• bicategory of relations

• Rel

• SEAR

• ETCR

• digraph

• loop digraph object

• Theory of units and tabulations in allegories

References

• Peter Freyd, Andre Scedrov:

  Categories, Allegories

  Mathematical Library Vol 39, North-Holland (1990).

  ISBN 978-0-444-70368-2