CatDat

Implication Details

Assumptions: cokernels, kernels, preadditive

Conclusions: quotients of congruences

Reason: For any congruence $E$ on an object $X$ of a preadditive category, let $E_0$ be the kernel of $p_2 : E \to X$. The restriction of $p_1$ to $E_0$ is a monomorphism. We can then see that $E$ must be the pullback of $p_1 - p_2 : E \to X$ and $E_0 \hookrightarrow X$. Then the cokernel of $E_0 \hookrightarrow X$ is a quotient of $E$.