Theorems · Theorem · category theory

CategoryTheory.Triangulated.SpectralObject.hom_ext

∀ {C : Type u_1} {ι : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} ι] [inst_2 : CategoryTheory.Limits.HasZeroObject C]
  [inst_3 : CategoryTheory.HasShift C ℤ] [inst_4 : CategoryTheory.Preadditive C]
  [inst_5 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_6 : CategoryTheory.Pretriangulated C]
  {X Y : CategoryTheory.Triangulated.SpectralObject C ι} {α β : X ⟶ Y}, α.hom = β.hom → α = β

Defined in: Mathlib.CategoryTheory.Triangulated.SpectralObject
Cited by: 1 results in Mathlib
Foundations: Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Limits.HasZeroObject CategoryTheory.HasShift CategoryTheory.Preadditive CategoryTheory.Functor.Additive CategoryTheory.Pretriangulated

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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.Homstatement and proof · cited by 32,603
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.Preadditivestatement and proof · cited by 3,309
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.Pretriangulatedstatement and proof · cited by 669
CategoryTheory.ComposableArrowsstatement · cited by 627
CategoryTheory.Triangulated.SpectralObjectstatement and proof · cited by 39
CategoryTheory.Triangulated.SpectralObject.ω₁statement · cited by 35

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Triangulated.SpectralObject.hom_ext_iffproof · cited by 0