Theorems · Theorem · group theory
Subgroup.map_id
∀ {G : Type u_1} [inst : Group G] (K : Subgroup G), Subgroup.map (MonoidHom.id G) K = K- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- SetLike.coe_injectiveproof · cited by 374
- MonoidHom.idstatement and proof · cited by 323
- Subgroup.mapstatement and proof · cited by 301
- Set.image_idproof · cited by 60
Cited by4
Results whose statement or proof uses this declaration.
- Subgroup.map_symm_eq_iff_map_eqproof · cited by 4
- Subgroup.normalCore_eq_iInf_map_conjproof · cited by 1
- Subgroup.commutator_prod_prodproof · cited by 1
- QuotientGroup.congr_reflstatement · cited by 0