Theorems · Theorem · category theory

CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_obj

∀ (C : Type u_1) [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.HasShift C ℤ]
  (T : CategoryTheory.Pretriangulated.Triangle Cᵒᵖ),
  (CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse C).obj T =
    Opposite.op
      (CategoryTheory.Pretriangulated.Triangle.mk T.mor₂.unop T.mor₁.unop
        (CategoryTheory.CategoryStruct.comp
          ((CategoryTheory.Pretriangulated.opShiftFunctorEquivalence C 1).unitIso.inv.app T.obj₁).unop
          ((CategoryTheory.shiftFunctor C 1).map T.mor₃.unop)))

Defined in

Mathlib.CategoryTheory.Triangulated.Opposite.Triangle

Cited by

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Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasShift