\begin{definition}[Definition:Kernel (Category Theory)/Definition 2]
Let $\mathbf C$ be a category.
Let $A$ and $B$ be objects of $\mathbf C$.
Let $f: A \to B $ be a morphism in $\mathbf C$.
Let $\mathbf C$ have a zero object $0$.
A '''kernel''' of $f$ is a morphism $\ker(f) \to A$, which is an equalizer of $f$ and the zero morphism $0: A \to B$.
\end{definition}