Theorems · Theorem · ring theory

BialgEquiv.trans_apply

∀ {R : Type u} {A : Type v} {B : Type w} {C : Type u₁} [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] (e₁₂ : A ≃ₐc[R] B)
  (e₂₃ : B ≃ₐc[R] C) (x : A), (e₁₂.trans e₂₃) x = ↑e₂₃ (↑e₁₂ x)

Defined in

Mathlib.RingTheory.Bialgebra.Equiv

Cited by

0 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringSemiringAlgebraAlgebraAlgebraCoalgebraStructCoalgebraStructCoalgebraStruct