Endofunctors of set determined by their object map (Q1417764)

A set functor \(F\) is called a DVO-functor if \(F\) is naturally equivalent to any set functor \(G\) such that \(|FX|=|GX|\) for any set \(X\). The author says that a set functor is finitary if \(|FX|=|X|\) for all infinite sets \(X\). The aim of this paper is to present two special classes of finitary DVO-set functors. One of the presented classes of finitary DVO-set functors is a modification of the power set functor.