Excisive

Definition 16.5.1. Let \(F\colon C \to D\) be a functor between \(\infty \)-categories.

(1)

If \(C\) admits pushouts, we say that \(F\) is excisive if it sends pushout squares in \(C\) to pullback squares in \(D\).

(2)

If \(C\) admits a terminal object, we say that \(F\) is reduced if it sends the terminal object of \(C\) to a terminal object of \(D\).

We write \(\Exc (C,D) \subseteq \Fun (C,D)\) for the full subcategory of excisive functors, \(\Fun _*(C,D) \subseteq \Fun (C,D)\) for the full subcategory of reduced functors, and \(\Exc _*(C,D)\) for their intersection.