The Clowder Project

Let $f\colon \webleft (X,x_{0}\webright )\to \webleft (Y,y_{0}\webright )$ be a morphism of pointed sets.

1. The morphism $f$ is active if $f^{-1}\webleft (y_{0}\webright )=x_{0}$.
2. The morphism $f$ is inert if, for each $y\in Y$, the set $f^{-1}\webleft (y\webright )$ has exactly one element.