Congruence in a Category

A congruence in a Category $\mathcal{C}$ is a sort of "internal equivalence relation" to $\mathcal{C}$. Explicitly, a congruence is a Jointly Monic Pair $X\xleftarrow{p_{1}}R\xrightarrow{p_{2}}X$ equipped with Morphism of Spans that witness reflexivity, symmetry, and transitivity.