triangleh — Mathlib

English

The triangle map in the identity case is the identity morphism on the triangle.

Русский

При тождественном случае треугольниковая карта есть тождественный морфизм.

LaTeX

$$$triangleMap(φ, φ) (id, id) = id$$$

Lean4

/-- The (distinguished) triangle in the homotopy category that is associated to
a morphism `φ : K ⟶ L` in the category `CochainComplex C ℤ`. -/
noncomputable abbrev triangleh : Triangle (HomotopyCategory C (ComplexShape.up ℤ)) :=
  (HomotopyCategory.quotient _ _).mapTriangle.obj (triangle φ)

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