Definition:Left Cancellable Mapping

Definition
A mapping $f: Y \to Z$ is left cancellable (or left-cancellable) if:


 * $\forall X: \forall g_1: X \to Y, g_2: X \to Y: f \circ g_1 = f \circ g_2 \implies g_1 = g_2$

Also known as left cancellative.

Also see

 * Right cancellable mapping

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