commGrpTypeEquivalenceCommGrpForgetCommMon

English

Compatibility between commutative group-equivalences and forgetful links to MonCat and MonTypeEquivalenceMon.

Русский

Совместимость эквивалентностей для коммутативных групп и забывачевых связей между MonCat и MonTypeEquivalenceMon.

LaTeX

$$$ commGrpTypeEquivalenceCommMonForgetCommMon \cong \text{Id} $$$

Lean4

/-- The equivalences `CommMon (Type u) ≌ CommMonCat.{u}` and `CommGrp_ (Type u) ≌ CommGrpCat.{u}`
are naturally compatible with the forgetful functors to `GrpCat` and `Grp_ (Type u)`.
-/
noncomputable def commGrpTypeEquivalenceCommGrpForgetCommMon :
    CommGrpTypeEquivalenceCommGrp.functor ⋙ forget₂ CommGrpCat CommMonCat ≅
      CommGrp_.forget₂CommMon (Type u) ⋙ CommMonTypeEquivalenceCommMon.functor :=
  Iso.refl _

Похожие утверждения