Theorems · Theorem · group theory
Con.kerLift_injective
∀ {M : Type u_1} {P : Type u_3} [inst : MulOneClass M] [inst_1 : MulOneClass P] (f : M →* P),
Function.Injective ⇑(Con.kerLift f)A monoid homomorphism f induces an injective homomorphism on the quotient by f's kernel.
- Defined in
- Mathlib.GroupTheory.Congruence.Hom
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- MulOneClassMulOneClass
Around this declaration
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- MonoidHomstatement and proof · cited by 3,629
- MulOneClassstatement and proof · cited by 1,018
- Con.Quotientstatement and proof · cited by 48
- Con.kerstatement and proof · cited by 24
- Quotient.inductionOn₂'proof · cited by 19
- Con.eqproof · cited by 9
- Con.kerLiftstatement · cited by 4
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