Example 2

Let A, B, C be topological spaces and let $u: A\rightarrow B$, $v: B\rightarrow C$ be continuous mappings; put $w=v\circ u$. Let E and $E'$ be C-spaces. The canonical morphism from $\mathscr{M}$or$_C(E; E')_A$ into $\mathscr{M}$or$_A(E_A; E'_A)$ is the composite morphism of the morphism $\mathscr{M}$or$_C(E; E')_A\rightarrow \mathscr{M}$or$_B(E_B; E'_B)_A$ deduced from the canonical morphism of $\mathscr{M}$or$_C(E; E')_B$ into $\mathscr{M}$or$_B(E_B; E'_B)$ and the canonical morphism of $\mathscr{M}$or$_B(E_B,E'_B)_A$ into $\mathscr{M}$or$_A(E_A,E'_A)$.