Notation 3.27.
Given \(n \geq 0\) and a morphism \(f\colon X \to Y\), write
\[\pi_n(f) \in (T_{/Y})_{/f} \cong T_{/X}\]
for the \(n\)-th homotopy object of \(f\) regarded as an object of \(T_{/Y}\). \emph{(Note: We do \underline{not} mean the induced map \(\pi_n(X) \to \pi_n(Y)\).)}