CatDat

• Notation: $(\Ab_{\fg},\otimes,\IZ)$
• Underlying category: category of finitely generated abelian groups
• Related symmetric monoidal categories: $(\Ab,\otimes,\IZ)$, $(\FinVect_K,\otimes,K)$

This is the full symmetric monoidal subcategory of $(\Ab,\otimes,\IZ)$ spanned by the finitely generated abelian groups. This is well-defined because $\IZ$ is finitely generated and the tensor product of two finitely generated abelian groups is finitely generated.