Theorems · Theorem · ring theory

TensorProduct.map_convMul_map

∀ {R : Type u_1} {A : Type u_3} {B : Type u_4} {C : Type u_5} [inst : CommSemiring R]
  [inst_1 : NonUnitalNonAssocSemiring A] [inst_2 : Module R A] [inst_3 : SMulCommClass R A A]
  [inst_4 : IsScalarTower R A A] [inst_5 : AddCommMonoid C] [inst_6 : Module R C] [inst_7 : CoalgebraStruct R C]
  {D : Type u_7} [inst_8 : AddCommMonoid B] [inst_9 : Module R B] [inst_10 : CoalgebraStruct R B]
  [inst_11 : NonUnitalNonAssocSemiring D] [inst_12 : Module R D] [inst_13 : SMulCommClass R D D]
  [inst_14 : IsScalarTower R D D] {f h : WithConv (C →ₗ[R] A)} {g k : WithConv (B →ₗ[R] D)},
  WithConv.toConv (TensorProduct.map f.ofConv g.ofConv) * WithConv.toConv (TensorProduct.map h.ofConv k.ofConv) =
    WithConv.toConv (TensorProduct.map (f * h).ofConv (g * k).ofConv)

Defined in

Mathlib.RingTheory.Coalgebra.Convolution

Cited by

0 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringNonUnitalNonAssocSemiringModuleSMulCommClassIsScalarTowerAddCommMonoidModuleCoalgebraStructAddCommMonoidModuleCoalgebraStructNonUnitalNonAssocSemiringModuleSMulCommClassIsScalarTower