Theorems · Theorem · ring theory

Algebra.TensorProduct.mapRingHom_comp_includeLeftRingHom

∀ {R : Type u_3} {S : Type u_4} {T : Type u_5} {R' : Type u_6} {S' : Type u_7} {T' : Type u_8} [inst : CommSemiring R]
  [inst_1 : CommSemiring S] [inst_2 : CommSemiring T] [inst_3 : Algebra R S] [inst_4 : Algebra R T]
  [inst_5 : CommSemiring R'] [inst_6 : CommSemiring S'] [inst_7 : CommSemiring T'] [inst_8 : Algebra R' S']
  [inst_9 : Algebra R' T'] (fR : R →+* R') (fS : S →+* S') (fT : T →+* T')
  (HS : fS.comp (algebraMap R S) = (algebraMap R' S').comp fR)
  (HT : fT.comp (algebraMap R T) = (algebraMap R' T').comp fR),
  (Algebra.TensorProduct.mapRingHom fR fS fT HS HT).comp Algebra.TensorProduct.includeLeftRingHom =
    Algebra.TensorProduct.includeLeftRingHom.comp fS

Defined in

Mathlib.RingTheory.TensorProduct.Maps

Cited by

1 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringCommSemiringAlgebraAlgebraCommSemiringCommSemiringCommSemiringAlgebraAlgebra