Theorems · Theorem · ring theory

IsGroupLikeElem.comul_eq_tmul_self

∀ {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid A] [inst_2 : Module R A]
  [inst_3 : Coalgebra R A] {a : A}, IsGroupLikeElem R a → CoalgebraStruct.comul a = a ⊗ₜ[R] a

A group-like element a satisfies Δ(a) = a ⊗ₜ a.

Defined in

Mathlib.RingTheory.Coalgebra.GroupLike

Cited by

13 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleCoalgebra