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Theorems · Theorem · ring theory

BialgHom.id_apply

∀ (R : Type u_1) (A : Type u_2) [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
  [inst_3 : CoalgebraStruct R A] (x : A), (BialgHom.id R A) x = x
Defined in
Mathlib.RingTheory.Bialgebra.Hom
Cited by
3 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringSemiringAlgebraCoalgebraStruct
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AddMonoidAlgebra.mapDomainBialgHom_id · cited by 1AddMonoidAlgebra.mapDomai…CommBialgCat.id_apply · cited by 0CommBialgCat.id_applyMonoidAlgebra.mapDomainBialgHom_id · cited by 0MonoidAlgebra.mapDomainBi…DFunLike.coe · cited by 62936DFunLike.coeSemiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringCoalgebraStruct · cited by 230CoalgebraStructBialgHom · cited by 190BialgHomBialgHom.id · cited by 22BialgHom.idBialgHom.id_applyCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.