Adámek, JiríSousa, LurdesTholen, Walter2015-07-302015-07-3020000010-2628http://hdl.handle.net/10400.19/2898Categories whose Yoneda embedding has a left adjoint are kmown as total categories and are characterized by a strong cocompleteness property. We introduce the notion of multitotal category A by asking the Yoneda embedding A --> [A^{op}, Set] to be right multiadjoint and prove that this property is equivalent to totality of the formal ptoduct completiom of A. We also characterize multitotal categories with various types of generators; in particular, the existence of dense generators is inherited by the formal product completion iff measurable cardinals cannot be arbitrarily large.engmultitotal categorymultisolid functorproduct completionjournal article