One obstruction for closedness
Categories whose Yoneda embedding has a left adjoint are known as total categories and are characterized by a strong cocompleteness property. We introduce the notion of multitotal category by asking the Yoneda embedding to be right multiadjoint and prove that this property is equivalent to totality of the formal product completion of . We also characterize multitotal categories with various types of generators; in particular, the existence of dense generators is inherited by the formal product...