Bijection iff Left and Right Inverse/Corollary
Corollary to Bijection iff Left and Right Inverse
Let $f: S \to T$ and $g: T \to S$ be mappings such that:
- $g \circ f = I_S$
- $f \circ g = I_T$
Then both $f$ and $g$ are bijections.
Suppose we have such mappings $f$ and $g$ with the given properties.
It directly follows that by setting $g = f, f = g_1, f = g_2$, the result Bijection iff Left and Right Inverse can be used the other way about.