nLab zero function

A zero function is a constant function whose constant value is zero.

Formally, if $X$ is a set and $Y$ is a pointed set with basepoint $0$, then the zero function from $X$ to $Y$ is

$$0\colon X \to Y\colon t \mapsto 0 .$$

If $X$ is also pointed, then the zero function must preserve basepoints, making this a case of a zero morphism. However, $X$ need not be pointed for the zero function to make sense.