eq_zero_of_hasInjectiveDimensionLT

English

The composite coimage.π f ≫ Abelian.factorThruImage f ≫ image.ι f equals f.

Русский

Составной путь coimage.π f ≫ Abelian.factorThruImage f ≫ image.ι f равен f.

LaTeX

$$$\mathrm{coimage.\pi}(f) \circ \mathrm{Abelian.factorThruImage}(f) \circ \mathrm{image.\iota}(f) = f$$$

Lean4

theorem eq_zero_of_hasInjectiveDimensionLT [HasExt.{w} C] {X Y : C} {i : ℕ} (e : Ext Y X i) (n : ℕ)
    [HasInjectiveDimensionLT X n] (hi : n ≤ i) : e = 0 :=
  (HasInjectiveDimensionLT.subsingleton X n i hi Y).elim _ _

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