Theorems · Theorem · ring theory

Coalgebra.TensorProduct.map_toLinearMap

∀ {R : Type u_5} {S : Type u_6} {M : Type u_7} {N : Type u_8} {P : Type u_9} {Q : Type u_10} [inst : CommSemiring R]
  [inst_1 : CommSemiring S] [inst_2 : Algebra R S] [inst_3 : AddCommMonoid M] [inst_4 : AddCommMonoid N]
  [inst_5 : AddCommMonoid P] [inst_6 : AddCommMonoid Q] [inst_7 : Module R M] [inst_8 : Module R N]
  [inst_9 : Module R P] [inst_10 : Module R Q] [inst_11 : Module S M] [inst_12 : IsScalarTower R S M]
  [inst_13 : Coalgebra S M] [inst_14 : Module S N] [inst_15 : IsScalarTower R S N] [inst_16 : Coalgebra S N]
  [inst_17 : Coalgebra R P] [inst_18 : Coalgebra R Q] (f : M →ₗc[S] N) (g : P →ₗc[R] Q),
  ↑(Coalgebra.TensorProduct.map f g) = TensorProduct.AlgebraTensorModule.map ↑f ↑g

Defined in

Mathlib.RingTheory.Coalgebra.TensorProduct

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraAddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleModuleModuleIsScalarTowerCoalgebraModuleIsScalarTowerCoalgebraCoalgebraCoalgebra