Theorems · Theorem · group theory
MonoidHom.comap_bot
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] (f : G →* N), Subgroup.comap f ⊥ = f.ker- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Bot.botstatement · cited by 4,720
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement · cited by 3,593
- MonoidHom.kerstatement · cited by 212
- Subgroup.comapstatement · cited by 154
Cited by6
Results whose statement or proof uses this declaration.
- Subgroup.index_kerproof · cited by 7
- Subgroup.ker_le_comapproof · cited by 5
- MonoidHom.ker_comp_of_injectiveproof · cited by 2
- MonoidHom.range_eq_bot_iffproof · cited by 1
- Subgroup.relIndex_kerproof · cited by 0
- MonoidHom.ker_prodMapproof · cited by 0