Final functors

Definition 21.5.2. A functor \(\alpha \) satisfying the conditions of the theorem is called final. We say that \(\alpha \) is initial if \(\alpha \catop \colon I\catop \to J\catop \) is final (i.e. each relative slice \(I_{/j}\) is weakly contractible, or equivalently limits of functors \(F\colon J \to C\) may be computed as limits of \(F \circ \alpha \colon I \to C\)).