Corollary 1

Let B be a topological space and A a subspace of B. Suppose that the spaces A and B are locally connected. Let E and $E'$ be coverings of B. Then the canonical morphisms $\psi :\mathscr{M}$or$_B(E; E')_A\rightarrow \mathscr{M}$or$_A(E_A; E'_A)$ and $\psi ':\mathscr{I}$som$_B(E; E')_A\rightarrow$ $\mathscr{I}$som$_A(E_A; E'_A)$ (I, p. 45, example 4) are isomorphisms.

For every point $a\in A$, it follows from the preceding proposition and from example 2 of I, p. 63, applied to the spaces $\{a\}$, A, B and to the canonical injections, that the canonical morphism $\psi$ induces on passing to the stalks the identity of $E^{E'_a}_a$. It is therefore an isomorphism. The fact that $\psi '$ is an isomorphism is proved analogously.