Theorems · Definition · category theory

CategoryTheory.Pretriangulated.contractibleTriangle

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.HasShift C ℤ] →
      [CategoryTheory.Limits.HasZeroObject C] →
        [CategoryTheory.Limits.HasZeroMorphisms C] → C → CategoryTheory.Pretriangulated.Triangle C

For each object in C, there is a triangle of the form (X,X,0,𝟙 X,0,0)

Defined in

Mathlib.CategoryTheory.Triangulated.Basic

Cited by

27 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.HasShiftCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphisms