[Merged by Bors] - feat(category_theory/abelian): biproducts of projective objects are projective #7319
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Co-authored-by: Bhavik Mehta <bhavikmehta8@gmail.com>
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| instance {P Q : C} [has_zero_morphisms C] [has_binary_biproduct P Q] | ||
| [projective P] [projective Q] : | ||
| projective (P ⊞ Q) := | ||
| { factors := λ E X' f e epi, by exactI | ||
| ⟨biprod.desc (factor_thru (biprod.inl ≫ f) e) (factor_thru (biprod.inr ≫ f) e), by tidy⟩, } |
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It would be nice if this didn't need to be separately stated, let alone proved, and Lean just knew that biproducts were coproducts, but it doesn't seem easy in our current setup. :-(
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Thanks 🎉 bors merge |
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…rojective (#7319) Also all objects of `Type` are projective. Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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Also all objects of
Typeare projective.