homEquiv — Mathlib

English

A variant of associativity when the middle Ext has degree zero.

Русский

Вариант ассоциации при нулевой степени в середине.

LaTeX

$$@[simp] theorem comp_assoc_of_second_deg_zero {a₁ a₂ a₁₂ : ℕ} (α : Ext X Y a₁) (β : Ext Y Z 0) (γ : Ext Z T a₃) (h₁₂ : a₁ + a₂ = a₁₂) :$$

Lean4

/-- When an instance of `[HasDerivedCategory.{w'} C]` is available, this is the bijection
between `Ext.{w} X Y n` and a type of morphisms in the derived category. -/
noncomputable def homEquiv {n : ℕ} :
    Ext.{w} X Y n ≃ ShiftedHom ((singleFunctor C 0).obj X) ((singleFunctor C 0).obj Y) (n : ℤ) :=
  SmallShiftedHom.equiv (HomologicalComplex.quasiIso C (ComplexShape.up ℤ)) Q

Похожие утверждения