nLab n-reduced (∞,1)-functor

Definition

In the context of Goodwillie calculus, an (∞,1)-functor is called $n$-reduced for $n \in \mathbb{N}$, $n \gt 0$, if its (n-1)-excisive approximation is trivial, $P_{n-1} F \simeq \ast$ (hence if it is a $P_{n-1}$ anti-modal type).

(e.g. Lurie, def. 6.1.2.1)

Hence a functor is 1-reduced (or just reduced, for short), if $F(\ast) \simeq \ast$.

A functor that is both n-excisive and $n$-reduced is called an n-homogeneous (∞,1)-functor.

References

• Jacob Lurie, section 6.1.1 of Higher Algebra