[Merged by Bors] - feat(category_theory/limits): products give pullback squares #14327
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semorrison
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I'll do biproducts giving bicartesian squares shortly. |
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May 23, 2022
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| def is_pushout_of_is_initial_is_coproduct {W X Y Z : C} (f : X ⟶ Z) (g : Y ⟶ Z) (h : W ⟶ X) | ||
| (k : W ⟶ Y) (H₁ : is_terminal Z) | ||
| (H₂ : is_limit (binary_fan.mk h k)) : | ||
| is_limit (pullback_cone.mk _ _ (show h ≫ f = k ≫ g, from H₁.hom_ext _ _)) := | ||
| (k : W ⟶ Y) (H₁ : is_initial W) | ||
| (H₂ : is_colimit (binary_cofan.mk f g)) : | ||
| is_colimit (pushout_cocone.mk _ _ (show h ≫ f = k ≫ g, from H₁.hom_ext _ _)) := |
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Apparently this had been copy-pasted ready for dualisation in #10581, but then only the declaration name was dualised!
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Merge conflict. |
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bors merge |
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May 25, 2022
Follow-up to #14220 Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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Follow-up to #14220 Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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Follow-up to #14220