instHasLiftingPropertyOfEpi — Mathlib

English

Given p : X → Y epi and P projective with HasZeroObject, and i : 0 → P, there is a HasLiftingProperty i p.

Русский

При p: X → Y эпимортым и P проективен с HasZeroObject, и i: 0 → P, существует HasLiftingProperty i p.

LaTeX

$$$ HasLiftingProperty(i,p) \\text{ follows from } [Epi(p)], [Projective(P)], [HasZeroObject(C)]. $$$

Lean4

instance {X Y P : C} (p : X ⟶ Y) [Epi p] [Projective P] [HasZeroObject C] (i : 0 ⟶ P) :
    HasLiftingProperty (i : 0 ⟶ P) p :=
  Projective.hasLiftingProperty_of_isZero i p (isZero_zero C)

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