Solution set

Set

context $ X $
context $ \langle Y,y_0 \rangle $ … pointed set
context $ f:X\to Y $
definition $ S := \{x\mid f(x)=y_0\}$

$S=f^{-1}(\{y_0\})$ where $f^{-1}:{\mathcal P}Y\to{\mathcal P}X$.

Reference

Wikipedia: Solution set

Context

Pointed set

Equalizer . category theory