Theorems · Theorem · commutative algebra

Algebra.Presentation.comp.congr_simp

∀ {R : Type u} {S : Type v} {ι : Type w} {σ : Type t} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  {ι' : Type u_1} {σ' : Type u_2} {T : Type u_3} [inst_3 : CommRing T] [inst_4 : Algebra S T]
  (Q Q_1 : Algebra.Presentation S T ι' σ'),
  Q = Q_1 →
    ∀ (P P_1 : Algebra.Presentation R S ι σ),
      P = P_1 → ∀ [inst_5 : Algebra R T] [inst_6 : IsScalarTower R S T], Q.comp P = Q_1.comp P_1

Defined in

Mathlib.RingTheory.Extension.Presentation.Submersive

Cited by

0 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTower