Exercise 4, § 2

Let A, B, C, D be four sets endowed with structures of the same species $\Sigma$, let $f$ be a morphism of A into B, $g$ a morphism of B into C, and $h$ a morphism of C into D. Show that if $g \circ f$ and $h \circ g$ are isomorphisms, then $f$, $g$, and $h$ are isomorphisms (cf. Chapter II, §3, Exercise 9).