Theorems · Theorem · group theory
AddSubgroup.comap_map_eq
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] (f : G →+ N) (H : AddSubgroup G),
AddSubgroup.comap f (AddSubgroup.map f H) = H ⊔ f.ker- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- le_antisymmproof · cited by 2,068
- map_addproof · cited by 964
- map_negproof · cited by 378
- neg_add_cancelproof · cited by 256
- AddSubgroup.mapstatement and proof · cited by 189
- sup_leproof · cited by 159
- AddMonoidHom.kerstatement and proof · cited by 158
- AddSubgroup.comapstatement and proof · cited by 123
Cited by8
Results whose statement or proof uses this declaration.
- AddSubgroup.index_mapproof · cited by 3
- AddSubgroup.map_injective_of_ker_leproof · cited by 2
- AddSubgroup.comap_map_eq_selfproof · cited by 2
- AddSubgroup.relIndex_map_mapproof · cited by 1
- AddSubgroup.IsFinitelyNormallyGenerated.comapproof · cited by 1
- AddSubgroup.map_le_map_iffproof · cited by 1
- QuotientAddGroup.comap_map_mk'proof · cited by 0
- AddCircle.denseRange_zsmul_coe_iffproof · cited by 0