Theorems · Inductive type · ring theory

BialgHom

(R : Type u_1) →
  (A : Type u_2) →
    (B : Type u_3) →
      [inst : CommSemiring R] →
        [inst_1 : Semiring A] →
          [inst_2 : Algebra R A] →
            [inst_3 : Semiring B] →
              [inst_4 : Algebra R B] → [CoalgebraStruct R A] → [CoalgebraStruct R B] → Type (max u_2 u_3)

Given R-algebras A, B with comultiplication maps Δ_A, Δ_B and counit maps ε_A, ε_B, an R-bialgebra homomorphism A →ₐc[R] B is an R-algebra map f such that ε_B ∘ f = ε_A and (f ⊗ f) ∘ Δ_A = Δ_B ∘ f.

Defined in

Mathlib.RingTheory.Bialgebra.Hom

Cited by

190 results in Mathlib

Foundations

Depth 19 from the axioms, rests on 182 definitions · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraSemiringAlgebraCoalgebraStructCoalgebraStruct