Theorems · Theorem · category theory

CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_map

∀ (C : Type u_1) [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.HasShift C ℤ]
  {T₁ T₂ : CategoryTheory.Pretriangulated.Triangle Cᵒᵖ} (φ : T₁ ⟶ T₂),
  (CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse C).map φ =
    Quiver.Hom.op { hom₁ := φ.hom₃.unop, hom₂ := φ.hom₂.unop, hom₃ := φ.hom₁.unop, comm₁ := ⋯, comm₂ := ⋯, comm₃ := ⋯ }

Defined in

Mathlib.CategoryTheory.Triangulated.Opposite.Triangle

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.HasShift