Corollary 2

Let $u': G''\rightarrow G'$ be a group homomorphism, and let $\mathscr{E}$ be a $\tau$-extension of G by F. Set $\tau ''=\tau '\circ u'$, and denote by $\varphi ($resp. $\varphi ',\varphi '')$ the canonical homomorphism associated with the $\tau '$-extension $u^*(\mathscr{E}) ($resp. the $\tau ''$-extension $u^{'*}(u^*(\mathscr{E}))$, the $\tau ''$-extension $(u\circ u')^*(\mathscr{E}))$. Then there exists a unique morphism $\psi$ from the $\tau ''$-extension $u^{'*}(u^*(\mathscr{E}))$ to the $\tau ''$-extension $(u\circ u')^*(\mathscr{E})$ such that $\varphi ''\circ \psi =\varphi \circ \varphi '$.