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916823d | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | 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
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