Axiomatic characterization of $\modsleft{\ZZ}$:

- There is a unit object $\one := \ZZ$ such that 
	- $\one$ is a [compact object of a category](compact object of a category.md)
	- $\one$ is a [projective object](projective object.md)
	- $\one$ [generates](generates.md) $\cat{C}$
	- $\Endo_{\cat C}(\one) \cong \ZZ$