Let \(U\) be a universe. We say a category \(C\) is lex \(U\)-cocomplete if the following conditions are satisfied.
- -\(C\) has finite limits.
- -\(C\) has \(U\)-small colimits.
- -\(U\)-small colimits in \(C\) satisfy descent.
Let \(U\) be a universe. We say a category \(C\) is lex \(U\)-cocomplete if the following conditions are satisfied.