instCoprod — Mathlib

English

The coproduct (binary) of two projective objects P and Q is projective.

Русский

Копроведение двух проективных объектов P и Q проективно.

LaTeX

$$$ \\text{Projective}(P \\oplus Q) \\quad \\text{for } P,Q \\text{ projective}. $$$

Lean4

instance {P Q : C} [HasBinaryCoproduct P Q] [Projective P] [Projective Q] : Projective (P ⨿ Q) where
  factors f e epi := ⟨coprod.desc (factorThru (coprod.inl ≫ f) e) (factorThru (coprod.inr ≫ f) e), by cat_disch⟩

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