Theorems · Definition · category theory

CategoryTheory.Pretriangulated.binaryBiproductTriangle

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.HasShift C ℤ] →
      (X₁ X₂ : C) →
        [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
          [CategoryTheory.Limits.HasBinaryBiproduct X₁ X₂] → CategoryTheory.Pretriangulated.Triangle C

The obvious triangle X₁ ⟶ X₁ ⊞ X₂ ⟶ X₂ ⟶ X₁⟦1⟧.

Defined in

Mathlib.CategoryTheory.Triangulated.Basic

Cited by

14 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasShiftCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproduct