Theorems · Theorem · ring theory

Bialgebra.TensorProduct.counit_eq_algHom_toLinearMap

∀ (R : Type u_1) (S : Type u_2) (A : Type u_3) (B : Type u_4) [inst : CommSemiring R] [inst_1 : CommSemiring S]
  [inst_2 : Semiring A] [inst_3 : Semiring B] [inst_4 : Bialgebra S A] [inst_5 : Bialgebra R B] [inst_6 : Algebra R A]
  [inst_7 : Algebra R S] [inst_8 : IsScalarTower R S A],
  CoalgebraStruct.counit =
    ((↑(Algebra.TensorProduct.rid R S S)).comp
        (Algebra.TensorProduct.map (Bialgebra.counitAlgHom S A) (Bialgebra.counitAlgHom R B))).toLinearMap

Defined in

Mathlib.RingTheory.Bialgebra.TensorProduct

Cited by

0 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringSemiringSemiringBialgebraBialgebraAlgebraAlgebraIsScalarTower