Theorems · Theorem · category theory

CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app

∀ {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),
  (CategoryTheory.shiftFunctorCompIsoId Cᵒᵖ n m hnm).inv.app X =
    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.shiftFunctor Cᵒᵖ m).map
          ((CategoryTheory.Pretriangulated.shiftFunctorOpIso C n m hnm).inv.app X)))

Defined in

Mathlib.CategoryTheory.Triangulated.Opposite.Basic

Cited by

2 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasShift