Your key objects are "customer" (a party who buys from you) "items" (individual things to buy), "shopping cart" (a collection of items associated with a specific customer). 

''What other objects -- "checkout manager"?''

A "credit card" object comes to mind ;-)

''Aha!  Payment!  What object is responsible for accepting payment?''

See ProvenSystemMetaphors, GenericBusinessFrameworkUnobtainable
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CategoryMetaphor