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Theorems · Definition · group theory

Con.comapQuotientEquiv

{M : Type u_1} →
  {N : Type u_2} →
    [inst : MulOneClass M] →
      [inst_1 : MulOneClass N] →
        (c : Con M) → (f : N →* M) → (Con.comap ⇑f ⋯ c).Quotient ≃* ↥(MonoidHom.mrange (c.mk'.comp f))

The second isomorphism theorem for monoids.

Defined in
Mathlib.GroupTheory.Congruence.Basic
Cited by
0 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MulOneClassMulOneClass
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

DFunLike.coe · cited by 62936DFunLike.coeMonoidHom · cited by 3629MonoidHomSubmonoid · cited by 3086SubmonoidMulEquiv · cited by 1142MulEquivMulOneClass · cited by 1018MulOneClassMonoidHom.comp · cited by 469MonoidHom.compCon · cited by 152ConMonoidHom.mrange · cited by 63MonoidHom.mrangeMulEquiv.trans · cited by 53MulEquiv.transCon.Quotient · cited by 48Con.QuotientMonoidHom.map_mul · cited by 37MonoidHom.map_mulMulEquiv.refl · cited by 33MulEquiv.reflCon.mk' · cited by 22Con.mk'Con.comap · cited by 15Con.comapCon.congr · cited by 2Con.congrCon.comapQuotientEquivCITED BYCITES

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