Theorems · Theorem · ring theory

AddMonoidAlgebra.comulAlgHom_comp_mapRingHom

∀ {R : Type u_1} {S : Type u_2} {M : Type u_8} [inst : CommSemiring R] [inst_1 : CommSemiring S]
  [inst_2 : AddCommMonoid M] (f : R →+* S),
  (Bialgebra.comulAlgHom S (AddMonoidAlgebra S M)).comp (AddMonoidAlgebra.mapRingHom M f) =
    (Algebra.TensorProduct.mapRingHom f (AddMonoidAlgebra.mapRingHom M f) (AddMonoidAlgebra.mapRingHom M f) ⋯ ⋯).comp
      (Bialgebra.comulAlgHom R (AddMonoidAlgebra R M)).toRingHom

Defined in: Mathlib.RingTheory.Bialgebra.MonoidAlgebra
Cited by: 0 results in Mathlib
Foundations: Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring CommSemiring AddCommMonoid

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites33

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

DFunLike.coeproof · cited by 62,936
AddCommMonoidstatement and proof · cited by 12,281
CommSemiringstatement and proof · cited by 10,911
RingHomstatement and proof · cited by 10,189
TensorProductstatement · cited by 2,545
TensorProduct.tmulproof · cited by 1,182
RingHom.compstatement and proof · cited by 899
map_oneproof · cited by 861
RingHomClass.toRingHomproof · cited by 746
AddMonoidAlgebrastatement and proof · cited by 649
AlgHom.toRingHomstatement and proof · cited by 490
MonoidHom.compproof · cited by 469

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.