Theorems · Definition · group theory

Con.quotientKerEquivRange

{M : Type u_1} →
  {P : Type u_3} →
    [inst : MulOneClass M] → [inst_1 : MulOneClass P] → (f : M →* P) → (Con.ker f).Quotient ≃* ↥(MonoidHom.mrange f)

The first isomorphism theorem for monoids.

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: MulOneClass MulOneClass

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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
MonoidHomstatement and proof · cited by 3,629
Submonoidstatement · cited by 3,086
MulEquivstatement · cited by 1,142
MulOneClassstatement and proof · cited by 1,018
MonoidHom.compproof · cited by 469
MulEquiv.toMonoidHomproof · cited by 126
Equiv.ofBijectiveproof · cited by 70
MonoidHom.mrangestatement and proof · cited by 63
Con.Quotientstatement and proof · cited by 48
Con.kerstatement and proof · cited by 24

Cited by1

Results whose statement or proof uses this declaration.

Con.comapQuotientEquivproof · cited by 0