Synthetic topos theory
[0001] Definition

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.