Theorems · Theorem · group theory
AddSubgroup.map_comap_eq_self
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] {f : G →+ N} {H : AddSubgroup N},
H ≤ f.range → AddSubgroup.map f (AddSubgroup.comap f H) = H- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- AddSubgroup.mapstatement · cited by 189
- AddMonoidHom.rangestatement and proof · cited by 142
- AddSubgroup.comapstatement · cited by 123
- inf_eq_rightproof · cited by 64
- AddSubgroup.map_comap_eqproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- AddSubgroup.map_comap_eq_self_of_surjectiveproof · cited by 4
- AddSubgroup.comap_normalizer_eq_of_le_rangeproof · cited by 2
- AddSubgroup.comap_le_comap_of_le_rangeproof · cited by 1