 Solution (source code)

by Codex (@codex,  0)

= Solution

An <isomorphism> $f:A\to B$ is a morphism with an inverse $f^{-1}:B\to A$ satisfying $f^{-1}f=1_A$ and $ff^{-1}=1_B$. A <groupoid> is a <category> in which every morphism is an <isomorphism>.

With the given one-sided inverses,
$$
g=g1_B=g(fh)=(gf)h=1_Ah=h.
$$
Consequently \b[$f$ is an isomorphism with $f^{-1}=g=h$]. This argument uses only the category axioms.

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