Theorems · Definition · group theory
AddSubgroup.inclusion
{G : Type u_1} → [inst : AddGroup G] → {H K : AddSubgroup G} → H ≤ K → ↥H →+ ↥KThe inclusion homomorphism from an additive subgroup H contained in K to K.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 · cited by 3,230
- AddMonoidHom.mk'proof · cited by 25
Cited by20
Results whose statement or proof uses this declaration.
- AddSubgroup.inclusion_injectivestatement · cited by 4
- AddSubgroup.quotientAddSubgroupOfEmbeddingOfLEproof · cited by 3
- AddSubgroup.card_dvd_of_leproof · cited by 2
- AddSubgroup.relIndex_addSubgroupOfproof · cited by 1
- AddSubgroup.inclusion_rangestatement · cited by 1
- SubAddAction.ofFixingAddSubgroup_of_inclusionstatement · cited by 1
- QuotientAddGroup.quotientMapAddSubgroupOfOfLeproof · cited by 1
- AddSubgroup.isAddCyclic_of_leproof · cited by 1
- AddSubgroup.inclusion_injstatement · cited by 0
- AddSubgroup.subtype_comp_inclusionstatement · cited by 0
- AddSubgroup.coe_inclusionstatement · cited by 0
- SubAddAction.ofFixingAddSubgroup_of_inclusion_injectivestatement · cited by 0