Theorems · Theorem · ring theory

LaurentPolynomial.comul_C_mul_T

∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Module R A]
  [inst_3 : Coalgebra R A] (a : A) (n : ℤ),
  CoalgebraStruct.comul (LaurentPolynomial.C a * LaurentPolynomial.T n) =
    (TensorProduct.map (AddMonoidAlgebra.lsingle n) (AddMonoidAlgebra.lsingle n)) (CoalgebraStruct.comul a)

Defined in: Mathlib.RingTheory.Coalgebra.MonoidAlgebra
Cited by: 1 results in Mathlib
Foundations: Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring Semiring Module Coalgebra

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

DFunLike.coestatement and proof · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
Semiringstatement and proof · cited by 13,802
CommSemiringstatement and proof · cited by 10,911
LinearMapstatement · cited by 10,215
RingHomstatement · cited by 10,189
TensorProductstatement · cited by 2,545
AddMonoidAlgebrastatement · cited by 649
TensorProduct.mapstatement and proof · cited by 250
CoalgebraStruct.comulstatement and proof · cited by 118
Coalgebrastatement and proof · cited by 112

Cited by1

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LaurentPolynomial.comul_C_mul_T_selfproof · cited by 0