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Theorems · Theorem · group theory

AddMonoidHom.range_eq_map

∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] (f : G →+ N), f.range = AddSubgroup.map f ⊤
Defined in
Mathlib.Algebra.Group.Subgroup.Ker
Cited by
15 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupAddGroup

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddMonoidHom.map_range · cited by 5AddMonoidHom.map_rangeAddSubgroup.top_subtype_lowerCentralSeries · cited by 4AddSubgroup.top_subtype_l…AddSubgroup.isAddCyclic_iff_exists_zmultiples_eq_top · cited by 4AddSubgroup.isAddCyclic_i…AddSubgroup.Normal.map · cited by 3Normal.mapAddSubgroup.map_le_range · cited by 2AddSubgroup.map_le_rangeAddGroup.nilpotent_of_surjective · cited by 2AddGroup.nilpotent_of_sur…AddSubgroup.map_subtype_addCommutator · cited by 2AddSubgroup.map_subtype_a…AddSubgroup.IsSubnormal.trans' · cited by 2IsSubnormal.trans'AddGroup.nilpotencyClass_le_of_surjective · cited by 1AddGroup.nilpotencyClass_…AddMonoid.Coprod.range_eq · cited by 1Coprod.range_eqAddEquiv.map_range_nsmulAddMonoidHom · cited by 1AddEquiv.map_range_nsmulA…AddMonoidHom.range_eq_bot_iff · cited by 1AddMonoidHom.range_eq_bot…AddSubgroup.map_eq_range_iff · cited by 1AddSubgroup.map_eq_range_…IsAddCyclic.card_nsmulAddMonoidHom_range · cited by 1IsAddCyclic.card_nsmulAdd…AddSubgroup.Normal.addCommutator_le_of_self_sup_commutative_eq_top · cited by 0Normal.addCommutator_le_o…DFunLike.coe · cited by 62936DFunLike.coeTop.top · cited by 9680Top.topAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupAddMonoidHom · cited by 3230AddMonoidHomAddSubgroup.map · cited by 189AddSubgroup.mapAddMonoidHom.range · cited by 142AddMonoidHom.rangeAddSubgroup.ext · cited by 75AddSubgroup.extAddSubgroup.mem_top · cited by 29AddSubgroup.mem_topAddMonoidHom.mem_range · cited by 16AddMonoidHom.mem_rangeAddSubgroup.mem_map · cited by 15AddSubgroup.mem_mapAddMonoidHom.range_eq_mapCITED BYCITES

Cites11

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Cited by15

Results whose statement or proof uses this declaration.