Theorems · Theorem · ring theory

isGroupLikeElem_iff

∀ (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.counit a = 1 ∧ CoalgebraStruct.comul a = a ⊗ₜ[R] a

Defined in

Mathlib.RingTheory.Coalgebra.GroupLike

Cited by

0 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleCoalgebra