Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.shiftClosure_eq_self

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (P : CategoryTheory.ObjectProperty C) {A : Type u_2}
  [inst_1 : AddMonoid A] [inst_2 : CategoryTheory.HasShift C A] [P.IsClosedUnderIsomorphisms] [P.IsStableUnderShift A],
  P.shiftClosure A = P

Defined in: Mathlib.CategoryTheory.ObjectProperty.Shift
Cited by: 4 results in Mathlib
Foundations: Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category AddMonoid CategoryTheory.HasShift CategoryTheory.ObjectProperty.IsClosedUnderIsomorphisms CategoryTheory.ObjectProperty.IsStableUnderShift

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objproof · cited by 19,642
CategoryTheory.Isoproof · cited by 3,963
AddMonoidstatement and proof · cited by 2,864
le_antisymmproof · cited by 2,068
CategoryTheory.shiftFunctorproof · cited by 1,553
CategoryTheory.HasShiftstatement and proof · cited by 1,527
CategoryTheory.Iso.symmproof · cited by 993
CategoryTheory.ObjectPropertystatement and proof · cited by 798
CategoryTheory.ObjectProperty.IsClosedUnderIsomorphismsstatement and proof · cited by 68
CategoryTheory.ObjectProperty.prop_of_isoproof · cited by 23
CategoryTheory.ObjectProperty.shiftClosurestatement and proof · cited by 17

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.ObjectProperty.shiftClosure_le_iffproof · cited by 2
CategoryTheory.ObjectProperty.shiftClosure_botproof · cited by 1
CategoryTheory.ObjectProperty.shiftClosure_topproof · cited by 0
CategoryTheory.ObjectProperty.isStableUnderShift_iff_shiftClosure_eq_selfproof · cited by 0