Theorems · Theorem · ring theory

BialgEquiv.trans_toCoalgEquiv

∀ {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}, ↑(e₁₂.trans e₂₃) = (↑e₁₂).trans ↑e₂₃

Defined in

Mathlib.RingTheory.Bialgebra.Equiv

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommSemiringSemiringSemiringSemiringAlgebraAlgebraAlgebraCoalgebraStructCoalgebraStructCoalgebraStruct