nLab
sink

Given an object $Y$ of a category $C$, a sink to $Y$ in $C$ is a collection of morphisms of $C$ whose targets (codomains) are all $Y$:

$$\begin{array}{c}{X}_1\\ & {\searrow }^{f_1}\\ X_2& \stackrel{f_2}{\to }& Y\\ & {\nearrow }_{f_3}\\ X_3\end{array}$$\array { X_1 \\ & \searrow^{f_1} \\ X_2 & \overset{f_2}\to & Y \\ & \nearrow_{f_3} \\ X_3 }

The dual concept is a collection of morphisms of $C$ whose sources (domains) are all $Y$:

$$\begin{array}{ccc}& & X_1\\ & {}^{f_1}\nearrow \\ Y& \stackrel{f_2}{\to }& X_2\\ & {}_{f_3}\searrow \\ & & X_3\end{array}$$\array { & & X_1 \\ & {}^{f_1}\nearrow \\ Y & \overset{f_2}\to & X_2 \\ & {}_{f_3}\searrow \\ & & X_3 }

Confusingly, this dual concept is called a source from $Y$ in $C$, even though the term ‘source’ has another meaning, one which we just used in the definition! One can of course say ‘domain’ instead of ‘source’ for this other meaning, but that leads to other confusions. Or one can say ‘cosink’ for a source in the sense dual to a sink, since a source from $Y$ in $C$ is the same as a sink to $Y$ in the opposite category $C^{\mathrm{op}}$.