nLab
fork

Idea

A fork is a diagram of the form

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

such that $f e=g e$. An example of a special type of a fork is an equalizer. Another example is a reflexive fork, where $C = A$ and $f e = 1_A$.

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

Related concepts

• monadicity theorem