## Franklin's Notes

### Coequalizer

A coequalizer is a colimit for a diagram of shape $\cdot\rightrightarrows\cdot$ in $\mathsf C$. Equivalently, a coequalizer of the morphisms $f,g$ of $\mathsf C$ can be thought of as a universal arrow from $\langle f,g\rangle$ to the diagonal functor $\Delta:\mathsf C\to\mathsf C^{\rightrightarrows}$.