Theorems · Theorem · ring theory

Bialgebra.TensorProduct.map_tmul

∀ {R : Type u_1} {S : Type u_2} {A : Type u_3} {B : Type u_4} {C : Type u_5} {D : Type u_6} [inst : CommSemiring R]
  [inst_1 : CommSemiring S] [inst_2 : Semiring A] [inst_3 : Semiring B] [inst_4 : Bialgebra S A]
  [inst_5 : Bialgebra R B] [inst_6 : Algebra R A] [inst_7 : Algebra R S] [inst_8 : IsScalarTower R S A]
  [inst_9 : Semiring C] [inst_10 : Semiring D] [inst_11 : Bialgebra S C] [inst_12 : Bialgebra R D]
  [inst_13 : Algebra R C] [inst_14 : IsScalarTower R S C] (f : A →ₐc[S] C) (g : B →ₐc[R] D) (x : A) (y : B),
  (Bialgebra.TensorProduct.map f g) (x ⊗ₜ[R] y) = f x ⊗ₜ[R] g y

Defined in

Mathlib.RingTheory.Bialgebra.TensorProduct

Cited by

0 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringSemiringSemiringBialgebraBialgebraAlgebraAlgebraIsScalarTowerSemiringSemiringBialgebraBialgebraAlgebraIsScalarTower