Definition 5.99.
Let \(n\geq 1\). A functor \(F\colon C\to T\) is called \(n\)-reduced if the map \(F\to *\) is a \(P_{n-1}\)-equivalence, or equivalently if \(P_{n-1}F\iso *\). More generally, a map \(F\to B\) is called \(n\)-reduced relative to \(B\) if it is a \(P_{n-1}\)-equivalence.
An \(n\)-excisive and \(n\)-reduced functor is called \(n\)-homogeneous.