Theorems · Theorem · category theory

CategoryTheory.Triangulated.SpectralObject.Hom.mk.inj

∀ {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} {hom : X.ω₁ ⟶ Y.ω₁}
  {comm :
    autoParam
      (∀ {i j k : ι} (f : i ⟶ j) (g : j ⟶ k),
        CategoryTheory.CategoryStruct.comp (X.δ f g)
            ((CategoryTheory.shiftFunctor C 1).map (hom.app (CategoryTheory.ComposableArrows.mk₁ f))) =
          CategoryTheory.CategoryStruct.comp (hom.app (CategoryTheory.ComposableArrows.mk₁ g)) (Y.δ f g))
      CategoryTheory.Triangulated.SpectralObject.Hom.comm._autoParam}
  {hom_1 : X.ω₁ ⟶ Y.ω₁}
  {comm_1 :
    autoParam
      (∀ {i j k : ι} (f : i ⟶ j) (g : j ⟶ k),
        CategoryTheory.CategoryStruct.comp (X.δ f g)
            ((CategoryTheory.shiftFunctor C 1).map (hom_1.app (CategoryTheory.ComposableArrows.mk₁ f))) =
          CategoryTheory.CategoryStruct.comp (hom_1.app (CategoryTheory.ComposableArrows.mk₁ g)) (Y.δ f g))
      CategoryTheory.Triangulated.SpectralObject.Hom.comm._autoParam},
  { hom := hom, comm := comm } = { hom := hom_1, comm := comm_1 } → hom = hom_1

Defined in

Mathlib.CategoryTheory.Triangulated.SpectralObject

Cited by

1 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound