Theorems · Definition · ring theory

CoalgEquiv.ofBijective

{R : Type u_1} →
  {A : Type u_2} →
    {B : Type u_3} →
      [inst : CommSemiring R] →
        [inst_1 : AddCommMonoid A] →
          [inst_2 : AddCommMonoid B] →
            [inst_3 : Module R A] →
              [inst_4 : Module R B] →
                [inst_5 : CoalgebraStruct R A] →
                  [inst_6 : CoalgebraStruct R B] → {f : A →ₗc[R] B} → Function.Bijective ⇑f → A ≃ₗc[R] B

Promotes a bijective coalgebra homomorphism to a coalgebra equivalence.

Defined in

Mathlib.RingTheory.Coalgebra.Equiv

Cited by

2 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModuleCoalgebraStructCoalgebraStruct