2-final 2-functors (Q2168813)

A functor \(F:C\to D\) is final if composition with \(F\) does not change colimits indexed on \(D\). A classical criterion for final functors states that \(F\) is final if and only if the slice category \(x/F\) is nonempty and connected for each object \(x\) in \(D\). The main theorem in this paper (Theorem 3.4) proves a 2-categorical analog: A 2-functor \(F:C\to D\) between small 2-categories is 2-final if and only if the slice 2-category \(x/F\) is nonempty, connected, and simply connected for each object \(x\) in \(D\).