commMonTypeEquivalenceCommMonForget

English

The forgetful functor forget MonCat to Type u is compatible with the equivalence Mon (Type u) ≌ MonCat, giving a natural isomorphism of forgetful composites.

Русский

Функтор забывания совместим с эквивалентностью Mon (Type u) ≌ MonCat, образуя естественную изomорфность композиции забывания.

LaTeX

$$$ \text{monTypeEquivalenceMonForget} : \text{Mon} \xrightarrow{forget} \text{Type} \cong \text{MonCat} \xrightarrow{equiv} \cdots $$$

Lean4

/-- The equivalences `Mon (Type u) ≌ MonCat.{u}` and `CommMon (Type u) ≌ CommMonCat.{u}`
are naturally compatible with the forgetful functors to `MonCat` and `Mon (Type u)`.
-/
noncomputable def commMonTypeEquivalenceCommMonForget :
    CommMonTypeEquivalenceCommMon.functor ⋙ forget₂ CommMonCat MonCat ≅
      CommMon.forget₂Mon (Type u) ⋙ MonTypeEquivalenceMon.functor :=
  Iso.refl _

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