Theorems · Theorem · category theory

CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.HasShift C ℤ] (X : Cᵒᵖ)
  (n m : ℤ) (hnm : autoParam (n + m = 0) CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app._auto_1)
  {Z : Cᵒᵖ} (h : (CategoryTheory.shiftFunctor Cᵒᵖ m).obj ((CategoryTheory.shiftFunctor Cᵒᵖ n).obj X) ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.shiftFunctorCompIsoId Cᵒᵖ n m hnm).inv.app X) h =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.shiftFunctorCompIsoId C m n ⋯).hom.app (Opposite.unop X)).op
      (CategoryTheory.CategoryStruct.comp
        ((CategoryTheory.Pretriangulated.shiftFunctorOpIso C m n ⋯).inv.app
          (Opposite.op ((CategoryTheory.shiftFunctor C m).obj (Opposite.unop X))))
        (CategoryTheory.CategoryStruct.comp
          ((CategoryTheory.shiftFunctor Cᵒᵖ m).map
            ((CategoryTheory.Pretriangulated.shiftFunctorOpIso C n m hnm).inv.app X))
          h))

Defined in

Mathlib.CategoryTheory.Triangulated.Opposite.Basic

Cited by

0 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasShift