Theorems · Theorem · ring theory

Prod.comul_apply

∀ (R : Type u) (A : Type v) (B : Type w) [inst : CommSemiring R] [inst_1 : AddCommMonoid A] [inst_2 : AddCommMonoid B]
  [inst_3 : Module R A] [inst_4 : Module R B] [inst_5 : Coalgebra R A] [inst_6 : Coalgebra R B] (r : A × B),
  CoalgebraStruct.comul r =
    (TensorProduct.map (LinearMap.inl R A B) (LinearMap.inl R A B)) (CoalgebraStruct.comul r.1) +
      (TensorProduct.map (LinearMap.inr R A B) (LinearMap.inr R A B)) (CoalgebraStruct.comul r.2)

Defined in

Mathlib.RingTheory.Coalgebra.Basic

Cited by

0 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModuleCoalgebraCoalgebra