Theorems · Definition · category theory

CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.HasShift C ℤ] →
      CategoryTheory.Functor (CategoryTheory.Pretriangulated.Triangle Cᵒᵖ) (CategoryTheory.Pretriangulated.Triangle C)ᵒᵖ

The functor which sends a triangle X ⟶ Y ⟶ Z ⟶ X⟦1⟧ in Cᵒᵖ to the triangle Z.unop ⟶ Y.unop ⟶ X.unop ⟶ Z.unop⟦1⟧ in C (without introducing signs).

Defined in

Mathlib.CategoryTheory.Triangulated.Opposite.Triangle

Cited by

13 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasShift