Mathlib Map

Theorems · Inductive type · ring theory

GroupLike

(R : Type u_2) →
  (A : Type u_3) →
    [inst : CommSemiring R] → [inst_1 : AddCommMonoid A] → [inst_2 : Module R A] → [Coalgebra R A] → Type u_3

The type of group-like elements in a coalgebra.

Defined in
Mathlib.RingTheory.Coalgebra.GroupLike
Cited by
19 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
CommSemiringAddCommMonoidModuleCoalgebra
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

GroupLike.val · cited by 16GroupLike.valGroupLike.toUnits · cited by 3GroupLike.toUnitsGroupLike.valEquiv · cited by 3GroupLike.valEquivGroupLike.casesOn · cited by 1GroupLike.casesOnGroupLike.ext · cited by 1GroupLike.extGroupLike.mk.inj · cited by 1mk.injGroupLike.mk.noConfusion · cited by 1mk.noConfusionGroupLike.isGroupLikeElem_val · cited by 1GroupLike.isGroupLikeElem…GroupLike.valMonoidHom · cited by 1GroupLike.valMonoidHomGroupLike.val_injective · cited by 1GroupLike.val_injectiveMonoidAlgebra.liftGroupLikeBialgHom · cited by 1MonoidAlgebra.liftGroupLi…GroupLike.ctorIdx · cited by 0GroupLike.ctorIdxGroupLike.ext_iff · cited by 0GroupLike.ext_iffGroupLike.mk.injEq · cited by 0mk.injEqGroupLike.mk.sizeOf_spec · cited by 0mk.sizeOf_specModule · cited by 20661ModuleAddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringCoalgebra · cited by 112CoalgebraGroupLikeCITED BYCITES

Cites4

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

Cited by30

Results whose statement or proof uses this declaration.