Theorems · Theorem · ring theory

Coalgebra.sum_counit_tmul_map_eq

∀ {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] {B : Type u_4} [inst_4 : AddCommMonoid B] [inst_5 : Module R B] {F : Type u_5}
  [inst_6 : FunLike F A B] [LinearMapClass F R A B] (f : F) (a : A) {repr : Coalgebra.Repr R a ι},
  ∑ i ∈ repr.index, CoalgebraStruct.counit (repr.left i) ⊗ₜ[R] f (repr.right i) = 1 ⊗ₜ[R] f a

Defined in

Mathlib.RingTheory.Coalgebra.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommSemiringAddCommMonoidModuleCoalgebraAddCommMonoidModuleFunLikeLinearMapClass