Theorems · Definition · group theory
Subgroup.comap
{G : Type u_1} → [inst : Group G] → {N : Type u_7} → [inst_1 : Group N] → (G →* N) → Subgroup N → Subgroup GThe preimage of a subgroup along a monoid homomorphism is a subgroup.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 154 results in Mathlib
- Foundations
- Depth 21 from the axioms, rests on 106 definitions · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Set.preimageproof · cited by 4,946
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Submonoidproof · cited by 3,086
- Submonoid.comapproof · cited by 179
- Subgroup.toSubmonoidproof · cited by 114
Cited by170
Results whose statement or proof uses this declaration.
- Subgroup.subgroupOfproof · cited by 122
- Matrix.GLPosproof · cited by 16
- QuotientGroup.mapstatement and proof · cited by 14
- Subgroup.map_le_iff_le_comapstatement · cited by 13
- Subgroup.gc_map_comapstatement · cited by 12
- Subgroup.comap_monostatement · cited by 11
- Subgroup.comap_topstatement · cited by 10
- Subgroup.comap_map_eqstatement and proof · cited by 9
- Subgroup.relIndex_comapstatement and proof · cited by 7
- Subgroup.comap_map_eq_self_of_injectivestatement · cited by 7
- Subgroup.Commensurable.commensuratorproof · cited by 7
- MonoidHom.comap_botstatement · cited by 6