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Theorems · Definition · ring theory

BialgEquiv.refl

(R : Type u) →
  (A : Type v) →
    [inst : CommSemiring R] →
      [inst_1 : Semiring A] → [inst_2 : Algebra R A] → [inst_3 : CoalgebraStruct R A] → A ≃ₐc[R] A

The identity map is a bialgebra equivalence.

Defined in
Mathlib.RingTheory.Bialgebra.Equiv
Cited by
7 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringSemiringAlgebraCoalgebraStruct
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

BialgEquiv.toHopfAlgIso_refl · cited by 0BialgEquiv.toHopfAlgIso_r…BialgEquiv.refl_apply · cited by 0BialgEquiv.refl_applyBialgEquiv.refl_toBialgHom · cited by 0BialgEquiv.refl_toBialgHomBialgEquiv.refl_toCoalgEquiv · cited by 0BialgEquiv.refl_toCoalgEq…BialgEquiv.toBialgIso_refl · cited by 0BialgEquiv.toBialgIso_reflCategoryTheory.Iso.toBialgEquiv_refl · cited by 0Iso.toBialgEquiv_reflCategoryTheory.Iso.toHopfAlgEquiv_refl · cited by 0Iso.toHopfAlgEquiv_reflSemiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringCoalgebraStruct · cited by 230CoalgebraStructBialgHom · cited by 190BialgHomBialgEquiv · cited by 88BialgEquivCoalgEquiv · cited by 77CoalgEquivBialgHom.id · cited by 22BialgHom.idCoalgEquiv.refl · cited by 7CoalgEquiv.reflBialgHom.map_mul' · cited by 0BialgHom.map_mul'BialgEquiv.reflCITED BYCITES

Cites10

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Cited by7

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