Theorems · Theorem · ring theory

BialgHom.comp_apply

∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} {C : Type u_4} [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : Semiring B] [inst_3 : Semiring C] [inst_4 : Algebra R A] [inst_5 : Algebra R B] [inst_6 : Algebra R C]
  [inst_7 : CoalgebraStruct R A] [inst_8 : CoalgebraStruct R B] [inst_9 : CoalgebraStruct R C] (φ₁ : B →ₐc[R] C)
  (φ₂ : A →ₐc[R] B) (x : A), (φ₁.comp φ₂) x = φ₁ (φ₂ x)

Defined in

Mathlib.RingTheory.Bialgebra.Hom

Cited by

6 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringSemiringAlgebraAlgebraAlgebraCoalgebraStructCoalgebraStructCoalgebraStruct