Exercise 1.5.5. Let \(F\colon C \hookrightarrow D\) be a monomorphism, and let \(y\) be an object of \(D\) which is contained in \(C\). Show that the fiber \(C_y\) of \(F\) at \(y\) is contractible.
Hint: Show that any functor \(x\colon * \to C_y\) is an equivalence by exhibiting it as a pullback of the equivalence \(\Delta _F\colon C \to C \times _D C\).
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