Definition:Right Cancellable Mapping

Definition
A mapping $f: X \to Y$ is right cancellable (or right-cancellable) iff:


 * $\forall Z: \forall \left({h_1,h_2: Y \to Z}\right): h_1 \circ f = h_2 \circ f \implies h_1 = h_2$

That is, if for any set $Z$:
 * If $h_1$ and $h_2$ are mappings from $Y$ to $Z$
 * then $h_1 \circ f = h_2 \circ f$ implies $h_1 = h_2$.

Also known as
Some sources call this a right cancellative mapping.

Also see

 * Definition:Left Cancellable Mapping
 * Surjection iff Right Cancellable

In the context of abstract algebra: from which it can be seen that a right cancellable mapping can be considered as a right cancellable element of an algebraic structure whose operation is composition of mappings.
 * Definition:Right Cancellable Element
 * Definition:Left Cancellable Element