Theorems · Theorem · group theory
QuotientGroup.con_ker_eq_conKer
∀ {G : Type u_1} {M : Type u_4} [inst : Group G] [inst_1 : Monoid M] (f : G →* M), QuotientGroup.con f.ker = Con.ker fThe congruence relation defined by the kernel of a group homomorphism is equal to its kernel as a congruence relation.
- Defined in
- Mathlib.GroupTheory.QuotientGroup.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- Monoidstatement and proof · cited by 3,887
- MonoidHomstatement and proof · cited by 3,629
- MonoidHom.kerstatement and proof · cited by 212
- Constatement and proof · cited by 152
- QuotientGroup.leftRelproof · cited by 61
- Con.kerstatement and proof · cited by 24
- QuotientGroup.leftRel_applyproof · cited by 17
- Setoid.comm'proof · cited by 9
- Con.extproof · cited by 8
- QuotientGroup.constatement · cited by 7
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