Monoid kernel
Set
| context | $ X $ |
| context | $ M $ … monoid |
| context | $ f:X\to M $ |
| definiendum | $ x\in\mathrm{ker}(f) $ |
| postulate | $ f(x)=e $ |
Discussion
$\mathrm{ker}(f)$ is $\mathrm{sol}(f)$ w.r.t. the unit of the monoid.
Reference
Wikipedia: Solution set
| context | $ X $ |
| context | $ M $ … monoid |
| context | $ f:X\to M $ |
| definiendum | $ x\in\mathrm{ker}(f) $ |
| postulate | $ f(x)=e $ |
$\mathrm{ker}(f)$ is $\mathrm{sol}(f)$ w.r.t. the unit of the monoid.
Wikipedia: Solution set