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This category contains definitions related to Surjections.
Related results can be found in Category:Surjections.

Let $S$ and $T$ be sets or classes.

Let $f: S \to T$ be a mapping from $S$ to $T$.

$f: S \to T$ is a surjection if and only if:

$\forall y \in T: \exists x \in \Dom f: \map f x = y$

That is, if and only if $f$ is right-total.