Theorems · Theorem · commutative algebra

RingHom.IsStableUnderBaseChange.pushout_inl

∀ {P : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop},
  RingHom.IsStableUnderBaseChange P →
    RingHom.RespectsIso P →
      ∀ {R S T : CommRingCat} (f : R ⟶ S) (g : R ⟶ T),
        P (CommRingCat.Hom.hom g) → P (CommRingCat.Hom.hom (CategoryTheory.Limits.pushout.inl f g))

Defined in: Mathlib.RingTheory.RingHomProperties
Cited by: 1 results in Mathlib
Foundations: Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites29

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

Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CommRingstatement and proof · cited by 17,173
Algebraproof · cited by 11,388
RingHomstatement and proof · cited by 10,189
CategoryTheory.NatTrans.appproof · cited by 7,406
CategoryTheory.Iso.invproof · cited by 6,514
TensorProductproof · cited by 2,545
CommRingCatstatement and proof · cited by 2,333
CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
CommRingCat.carrierstatement and proof · cited by 1,096
CategoryTheory.Limits.Cocone.ιproof · cited by 605

Cited by1

Results whose statement or proof uses this declaration.

RingHom.IsStableUnderBaseChange.pullback_fst_appTopproof · cited by 2