Theorems · Theorem · ring theory

Coalgebra.sum_counit_smul

∀ {R : Type u} {A : Type v} {ι : Type u_1} [inst : CommSemiring R] [inst_1 : AddCommMonoid A] [inst_2 : Module R A]
  [inst_3 : Coalgebra R A] {a : A} (𝓡 : Coalgebra.Repr R a ι),
  ∑ x ∈ 𝓡.index, CoalgebraStruct.counit (𝓡.left x) • 𝓡.right x = a

Defined in

Mathlib.RingTheory.Coalgebra.Basic

Cited by

1 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleCoalgebra