| import Mathlib | |
| open CategoryTheory | |
| namespace CAT_statement_S_0035 | |
| structure Construct where | |
| C : Type u | |
| [str : Category.{v} C] | |
| U : C ⥤ Type u | |
| [faithful : Functor.Faithful U] | |
| attribute [instance] Construct.str Construct.faithful | |
| def IsRealization (S T : Construct.{u, v}) (F : S.C ⥤ T.C) : Prop := | |
| F ⋙ T.U = S.U ∧ Functor.Full F ∧ Function.Injective F.obj | |
| theorem exists_universal_construct : | |
| ∃ (T : Construct.{u, v}), ∀ (S : Construct.{u, v}), ∃ (F : S.C ⥤ T.C), IsRealization S T F := by | |
| sorry | |
| end CAT_statement_S_0035 | |