Endofunctors of Set Determined by Their Object Map

Functors uniquely determined by their object map are called DVO functors. In this paper, we continue the research into DVO endofunctors of the category Set of all sets and maps as started by V. Trnková, R. El Bashir and A. Barkhudaryan. Two families of connected DVO functors containing an isomorphic copy of the identity functor Id are described.