Theorems · Definition · group theory

AddCon.quotientKerEquivRange

{M : Type u_1} →
  {P : Type u_3} →
    [inst : AddZeroClass M] →
      [inst_1 : AddZeroClass P] → (f : M →+ P) → (AddCon.ker f).Quotient ≃+ ↥(AddMonoidHom.mrange f)

The first isomorphism theorem for AddMonoids.

Defined in: Mathlib.GroupTheory.Congruence.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddZeroClass AddZeroClass

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Cites16

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Equivproof · cited by 8,337
AddMonoidHomstatement and proof · cited by 3,230
AddZeroClassstatement and proof · cited by 1,237
AddSubmonoidstatement · cited by 1,178
AddEquivstatement · cited by 1,087
AddMonoidHom.compproof · cited by 339
AddEquiv.toAddMonoidHomproof · cited by 101
Equiv.ofBijectiveproof · cited by 70
AddMonoidHom.mrangestatement and proof · cited by 61
AddCon.Quotientstatement and proof · cited by 54
AddCon.kerstatement and proof · cited by 24

Cited by1

Results whose statement or proof uses this declaration.

AddCon.comapQuotientEquivproof · cited by 0