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Theorems · Theorem · commutative algebra

CommRingCat.inl_injective_of_flat

∀ {R S T : CommRingCat} (f : R ⟶ S) (g : R ⟶ T),
  (CommRingCat.Hom.hom f).Flat →
    Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom g) →
      Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.pushout.inl f g))
Defined in
Mathlib.RingTheory.RingHom.Flat
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Foundations
Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
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DFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compAlgebra · cited by 11388AlgebraRingHom · cited by 10189RingHomCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homCommRingCat · cited by 2333CommRingCatCategoryTheory.Limits.WalkingPair · cited by 1319Limits.WalkingPairCommRingCat.carrier · cited by 1096CommRingCat.carrierCommRingCat.Hom.hom · cited by 432Hom.homRingHom.toAlgebra · cited by 337RingHom.toAlgebraCategoryTheory.Limits.WalkingSpan · cited by 300Limits.WalkingSpanCategoryTheory.Limits.span · cited by 294Limits.spanCategoryTheory.Limits.pushout · cited by 284Limits.pushoutCommRingCat.inl_injective_of_…CITED BYCITES

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