nLab
fork

A fork is a diagram of the form

$$A\underset{e}{\to }B\underset{g}{\overset{f}{\rightrightarrows }}C$$A\underset{\quad e \quad}{\to}B\underoverset{\quad g \quad}{f}{\rightrightarrows}C

such that $fe=ge$. An example of a special type of a fork is an equalizer.

A dual notion is also called a fork, but some people distinguish forks and coforks.