Theorems · Definition · commutative algebra

Algebra.Generators.Hom.comp

{R : Type u} →
  {S : Type v} →
    {ι : Type w} →
      [inst : CommRing R] →
        [inst_1 : CommRing S] →
          [inst_2 : Algebra R S] →
            {P : Algebra.Generators R S ι} →
              {R' : Type u_1} →
                {S' : Type u_2} →
                  {ι' : Type u_3} →
                    [inst_3 : CommRing R'] →
                      [inst_4 : CommRing S'] →
                        [inst_5 : Algebra R' S'] →
                          {P' : Algebra.Generators R' S' ι'} →
                            {R'' : Type u_4} →
                              {S'' : Type u_5} →
                                {ι'' : Type u_6} →
                                  [inst_6 : CommRing R''] →
                                    [inst_7 : CommRing S''] →
                                      [inst_8 : Algebra R'' S''] →
                                        {P'' : Algebra.Generators R'' S'' ι''} →
                                          [inst_9 : Algebra R' R''] →
                                            [inst_10 : Algebra R' S''] →
                                              [inst_11 : Algebra S S'] →
                                                [inst_12 : Algebra S' S''] →
                                                  [inst_13 : Algebra S S''] →
                                                    [IsScalarTower R' R'' S''] →
                                                      [IsScalarTower R' S' S''] →
                                                        [IsScalarTower S S' S''] → P'.Hom P'' → P.Hom P' → P.Hom P''

The composition of two homs.

Defined in

Mathlib.RingTheory.Extension.Generators

Cited by

6 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingCommRingAlgebraCommRingCommRingAlgebraAlgebraAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTowerIsScalarTower