Theorems · Theorem · commutative algebra

CommRingCat.closure_range_union_range_eq_top_of_isPushout

∀ {R A B X : CommRingCat} {f : R ⟶ A} {g : R ⟶ B} {a : A ⟶ X} {b : B ⟶ X},
  CategoryTheory.IsPushout f g a b →
    Subring.closure
        (Set.range ⇑(CategoryTheory.ConcreteCategory.hom a) ∪ Set.range ⇑(CategoryTheory.ConcreteCategory.hom b)) =
      ⊤

Defined in: Mathlib.Algebra.Category.Ring.Constructions
Cited by: 1 results in Mathlib
Foundations: Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
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CategoryTheory.CategoryStruct.compproof · cited by 17,999
Algebraproof · cited by 11,388
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CategoryTheory.Iso.invproof · cited by 6,514
Set.rangestatement and proof · cited by 4,705
CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
LE.le.transproof · cited by 3,151
TensorProductproof · cited by 2,545

Cited by1

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CommRingCat.HomTopology.isEmbedding_pushoutproof · cited by 0