Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.trW_monotone

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroObject C]
  [inst_2 : CategoryTheory.HasShift C ℤ] [inst_3 : CategoryTheory.Preadditive C]
  [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_5 : CategoryTheory.Pretriangulated C]
  {P Q : CategoryTheory.ObjectProperty C}, P ≤ Q → P.trW ≤ Q.trW

Defined in: Mathlib.CategoryTheory.Triangulated.Subcategory
Cited by: 1 results in Mathlib
Foundations: Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroObject CategoryTheory.HasShift CategoryTheory.Preadditive CategoryTheory.Functor.Additive CategoryTheory.Pretriangulated

Mathlib docs Source Loogle LeanSearch

Around this declaration

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
Quiver.Homproof · cited by 32,603
CategoryTheory.Functor.objproof · cited by 19,642
CategoryTheory.Preadditivestatement and proof · cited by 3,309
CategoryTheory.MorphismPropertystatement · cited by 2,179
CategoryTheory.shiftFunctorstatement and proof · cited by 1,553
CategoryTheory.HasShiftstatement and proof · cited by 1,527
CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
CategoryTheory.Functor.Additivestatement and proof · cited by 1,179
CategoryTheory.ObjectPropertystatement and proof · cited by 798
CategoryTheory.Pretriangulatedstatement and proof · cited by 669
CategoryTheory.Pretriangulated.distinguishedTrianglesproof · cited by 316

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.ObjectProperty.isVerdierRightLocalizing_iffproof · cited by 2