Theorems · Theorem · group theory
Con.kerLift_range_eq
∀ {M : Type u_1} {P : Type u_3} [inst : MulOneClass M] [inst_1 : MulOneClass P] {f : M →* P},
MonoidHom.mrange (Con.kerLift f) = MonoidHom.mrange fGiven a monoid homomorphism f, the induced homomorphism on the quotient by f's kernel has
the same image as f.
- Defined in
- Mathlib.GroupTheory.Congruence.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MulOneClassMulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MonoidHomstatement and proof · cited by 3,629
- Submonoidstatement · cited by 3,086
- MulOneClassstatement and proof · cited by 1,018
- MonoidHom.mrangestatement · cited by 63
- Con.Quotientstatement · cited by 48
- Con.kerstatement · cited by 24
- Con.kerLiftstatement · cited by 4
- Con.lift_rangeproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Con.quotientKerEquivRangeproof · cited by 0