Triangle-closure conditions on opposite subcategories #
Third-object closure of an object property in a pretriangulated category gives first-object closure of the opposite property. This instance allows arguments using first-object closure to be applied to the opposite category.
instance
CategoryTheory.ObjectProperty.instIsTriangulatedClosed₁OppositeOpOfIsTriangulatedClosed₃_tauCeti
{C : Type u}
[Category.{v, u} C]
[Limits.HasZeroObject C]
[Preadditive C]
[HasShift C ℤ]
[∀ (n : ℤ), (shiftFunctor C n).Additive]
[Pretriangulated C]
(P : ObjectProperty C)
[P.IsTriangulatedClosed₃]
:
Third-object closure of a property becomes first-object closure on the opposite category.