Definition 12.5.3. Let $f : x \to y$ be a morphism in an abelian category.

1. We say $f$ is injective if $\mathop{\mathrm{Ker}}(f) = 0$.

2. We say $f$ is surjective if $\mathop{\mathrm{Coker}}(f) = 0$.

If $x \to y$ is injective, then we say that $x$ is a subobject of $y$ and we use the notation $x \subset y$. If $x \to y$ is surjective, then we say that $y$ is a quotient of $x$.

There are also:

• 3 comment(s) on Section 12.5: Abelian categories

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).