\begin{definition}[Definition:Left Cancellable Mapping]
A mapping $f: Y \to Z$ is '''left cancellable''' (or '''left-cancellable''') {{iff}}:
:$\forall X: \forall \struct {g_1, g_2: X \to Y}: f \circ g_1 = f \circ g_2 \implies g_1 = g_2$
That is, for any set $X$, if $g_1$ and $g_2$ are mappings from $X$ to $Y$:
:If $f \circ g_1 = f \circ g_2$
:then $g_1 = g_2$.
\end{definition}