Category:Definitions/Class Mappings

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

Let $S$ and $T$ be classes.

A class mapping $f$ from $S$ to $T$, denoted $f: S \to T$, is a class relation $f = \mathcal R \subseteq S \times T$ such that:

$\forall x \in S: \forall y_1, y_2 \in T: \left({x, y_1}\right) \in f \land \left({x, y_2}\right) \in f \implies y_1 = y_2$

and

$\forall x \in S: \exists y \in T: \left({x, y}\right) \in f$