What is concrete equivalence?

The notion of concrete equivalence is introduced, based on a modification of the traditional notion of concrete functor. The discussion of examples includes a direct (i.e. not referring to any monadicity theorem) proof of the fact that monadicity is stable under concrete equivalence.For the sixtieth birthday of Nico PumplünHospitality of the Department of Mathematics, Applied Mathematics and Astronomy at UNISA is gratefully acknowledged, where this note was completed during an extended visit.