Let \(U\) be a universe and let \(C\) and \(D\) be lex \(U\)-cocomplete categories. We say a functor \(F:C\rightarrow D\) is a morphism of lex \(U\)-cocomplete categories if the following conditions are satisfied.

• -\(F\) commutes with finite limits.
• -\(F\) commutes with \(U\)-small colimits.