Theorems · Definition · commutative algebra

Algebra.PreSubmersivePresentation.comp

{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 R T] →
                        [inst_5 : Algebra S T] →
                          [IsScalarTower R S T] →
                            Algebra.PreSubmersivePresentation S T ι' σ' →
                              Algebra.PreSubmersivePresentation R S ι σ →
                                Algebra.PreSubmersivePresentation R T (ι' ⊕ ι) (σ' ⊕ σ)

Given an R-algebra S and an S-algebra T with pre-submersive presentations, this is the canonical pre-submersive presentation of T as an R-algebra.

Defined in

Mathlib.RingTheory.Extension.Presentation.Submersive

Cited by

6 results in Mathlib

Foundations

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

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTower