Theorems · Theorem · group theory
AddMonoidHom.range_eq_bot_iff
∀ {G : Type u_1} {G' : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup G'] {f : G →+ G'}, f.range = ⊥ ↔ f = 0- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Bot.botstatement and proof · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- top_le_iffproof · cited by 175
- AddMonoidHom.rangestatement · cited by 142
- le_bot_iffproof · cited by 116
- AddMonoidHom.range_eq_mapproof · cited by 15
- AddSubgroup.map_le_iff_le_comapproof · cited by 10
- AddMonoidHom.comap_botproof · cited by 6
- AddMonoidHom.ker_eq_top_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddGroup.isAddCyclic_of_coprime_card_range_card_kerproof · cited by 1