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Theorems · Theorem · group theory

AddMonoidHom.comap_ker

∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] {P : Type u_8} [inst_2 : AddZeroClass P]
  (g : N →+ P) (f : G →+ N), AddSubgroup.comap f g.ker = (g.comp f).ker
Defined in
Mathlib.Algebra.Group.Subgroup.Ker
Cited by
4 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Quot.sound
Assumes
AddGroupAddGroupAddZeroClass
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Around this declaration

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

QuotientAddGroup.ker_lift · cited by 2QuotientAddGroup.ker_liftAddMonoidHom.ker_comp_of_injective · cited by 1AddMonoidHom.ker_comp_of_…AddGroup.IsFinitelyPresented.of_surjective · cited by 1IsFinitelyPresented.of_su…AddMonoidHom.ker_comp_addEquiv · cited by 0AddMonoidHom.ker_comp_add…AddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupAddMonoidHom · cited by 3230AddMonoidHomAddZeroClass · cited by 1237AddZeroClassAddMonoidHom.comp · cited by 339AddMonoidHom.compAddMonoidHom.ker · cited by 158AddMonoidHom.kerAddSubgroup.comap · cited by 123AddSubgroup.comapAddMonoidHom.comap_kerCITED BYCITES

Cites7

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Cited by4

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