Michael: in informal math, a perfectly fine object of \$$\mathbf{ Set}\$$ is

$\\{ \text{Michael}, \text{Keith} \\} .$

This doesn't seem very abstract to me.

In more formal set theory we might identify you by numbers. That's a bit more abstract... but remember, computers do something similar, encoding everything as bit strings.

The objects of our database schema are what I'd call _really_ abstract. The database, \$$F\$$, sends these objects to sets, which I'd consider 'concrete'.