Theorems · Definition · ring theory

BialgEquiv.trans

{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] → (A ≃ₐc[R] B) → (B ≃ₐc[R] C) → A ≃ₐc[R] C

Bialgebra equivalences are transitive.

Defined in

Mathlib.RingTheory.Bialgebra.Equiv

Cited by

8 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringSemiringAlgebraAlgebraAlgebraCoalgebraStructCoalgebraStructCoalgebraStruct