Closure operators and shifts #
In this file, we collect facts relating being stable under shifts with closure properties of object properties.
instance
CategoryTheory.ObjectProperty.instIsStableUnderShiftRetractClosure
{C : Type u_1}
[Category.{v_1, u_1} C]
(P : ObjectProperty C)
{A : Type u_2}
[AddMonoid A]
[HasShift C A]
[P.IsStableUnderShift A]
:
instance
CategoryTheory.ObjectProperty.instIsStableUnderShiftLimitsClosure
{C : Type u_1}
[Category.{v_1, u_1} C]
(P : ObjectProperty C)
{A : Type u_2}
[AddGroup A]
[HasShift C A]
{α : Type u_3}
{J : α → Type u_4}
[(i : α) → Category.{u_5, u_4} (J i)]
[P.IsStableUnderShift A]
:
(P.limitsClosure J).IsStableUnderShift A