Axiomatic characterization of \({}_{{\mathbf{Z}}}{\mathsf{Mod}}\):
-
There is a unit object \(\one := {\mathbf{Z}}\) such that
- \(\one\) is a compact object of a category
- \(\one\) is a projective object
- \(\one\) generates \(\mathsf{C}\)
- \({ \operatorname{End} }_{\mathsf{C}}(\one) \cong {\mathbf{Z}}\)