Theorems · Definition · ring theory

Coalgebra.Repr.induced

{R : Type u} →
  {A : Type v} →
    {B : Type w} →
      {ι : Type u_1} →
        [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] →
                      {a : A} →
                        Coalgebra.Repr R a ι →
                          {F : Type u_2} →
                            [inst_7 : FunLike F A B] → [CoalgHomClass F R A B] → (φ : F) → Coalgebra.Repr R (φ a) ι

If φ : A → B is a coalgebra map and a = ∑ xᵢ ⊗ yᵢ, then φ a = ∑ φ xᵢ ⊗ φ yᵢ

Defined in

Mathlib.RingTheory.Coalgebra.Hom

Cited by

3 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModuleCoalgebraCoalgebraFunLikeCoalgHomClass