Contents

category theory

# Contents

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