Theorems · Theorem · group theory
Subgroup.map_comap_eq
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] (f : G →* N) (H : Subgroup N),
Subgroup.map f (Subgroup.comap f H) = f.range ⊓ H- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Set.imageproof · cited by 5,609
- Set.rangeproof · cited by 4,705
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- MonoidHom.rangestatement and proof · cited by 314
- Subgroup.mapstatement · cited by 301
- Set.inter_commproof · cited by 291
- Subgroup.comapstatement and proof · cited by 154
Cited by5
Results whose statement or proof uses this declaration.
- Subgroup.map_comap_eq_selfproof · cited by 3
- Subgroup.subgroupOf_supproof · cited by 2
- Subgroup.comap_sup_eq_of_le_rangeproof · cited by 1
- Subgroup.comap_eq_kerproof · cited by 1
- Subgroup.relIndex_inter_ne_zeroproof · cited by 0