Theorems · Definition · category theory

CategoryTheory.Triangulated.SpectralObject.Hom.mk.noConfusion

{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} →
                    {P : Sort u} →
                      {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' : 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 := hom, comm := comm } = { hom := hom', comm := comm' } → (hom ≍ hom' → P) → P

Defined in

Mathlib.CategoryTheory.Triangulated.SpectralObject

Cited by

1 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound