Corollary 3.2.5.7. Let $f: (X,x) \rightarrow (S,s)$ be a Kan fibration between pointed Kan complexes. Then the image of the induced map $\pi _{1}(f): \pi _1(X,x) \rightarrow \pi _{1}(S,s)$ is equal to the stabilizer of $[x] \in \pi _0(X_ s)$ (with respect to the action of $\pi _{1}(S,s)$ on $\pi _0(X_ s)$ supplied by Variant 3.2.4.5.

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