The forgetful functor from ℤ-modules to additive commutative groups is an equivalence of categories.

TODO: either use this equivalence to transport the monoidal structure from Module ℤ to Ab, or, having constructed that monoidal structure directly, show this functor is monoidal.

instance ModuleCat.forget₂_addCommGroup_full : CategoryTheory.Functor.Full (CategoryTheory.forget₂ (ModuleCat ℤ) AddCommGroupCat)

The forgetful functor from ℤ modules to AddCommGroup is full.

Equations

• ModuleCat.forget₂_addCommGroup_full = ⋯

instance ModuleCat.forget₂_addCommGroupCat_essSurj : CategoryTheory.Functor.EssSurj (CategoryTheory.forget₂ (ModuleCat ℤ) AddCommGroupCat)

The forgetful functor from ℤ modules to AddCommGroup is essentially surjective.

Equations

• ModuleCat.forget₂_addCommGroupCat_essSurj = ⋯

noncomputable instance ModuleCat.forget₂AddCommGroupIsEquivalence : CategoryTheory.Functor.IsEquivalence (CategoryTheory.forget₂ (ModuleCat ℤ) AddCommGroupCat)

Equations

• ModuleCat.forget₂AddCommGroupIsEquivalence = CategoryTheory.Functor.IsEquivalence.ofFullyFaithfullyEssSurj (CategoryTheory.forget₂ (ModuleCat ℤ) AddCommGroupCat)