instHasLiftingPropertyOfMono — Mathlib

English

If i is mono, I has injective, and there is a morphism p: I → 0, then HasLiftingProperty i p.

Русский

Если i моно, I инъективен, и есть p: I → 0, то HasLiftingProperty i p.

LaTeX

$$$$\\forall i:A\\to B\\;[\\text{Mono}(i)]\\;[\\text{Injective}(I)]\\;[\\text{HasZeroObject}]\; (p:I\\to 0)\\;\\Rightarrow \\; \\text{HasLiftingProperty}(i,p).$$$$

Lean4

instance {A B I : C} (i : A ⟶ B) [Mono i] [Injective I] [HasZeroObject C] (p : I ⟶ 0) :
    HasLiftingProperty i (p : I ⟶ 0) :=
  Injective.hasLiftingProperty_of_isZero i p (isZero_zero C)

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