Construction 3.2.4.3 (The Connecting Homomorphism). Let $f: (X,x) \rightarrow (S,s)$ be a Kan fibration between pointed Kan complexes. For each $n \geq 0$, we will refer to the map $\partial : \pi _{n+1}(S,s) \rightarrow \pi _{n}(X_ s, x)$ of Proposition 3.2.4.2 as the *connecting homomorphism* (for $n \geq 1$, it is a group homomorphism: see Proposition 3.2.4.4 below).

$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$