The very concept of "map" is abstract.
Then suggest me a better word for something like "beauty" or "happiness", because those are NOT physical or even mental.
Those are properties that are merely perceived when attached to physical objects, but this attachment in no way defines the property itself.
Not too dissimilar (in a certain sense) from how "electricity" is NOT "moving electrons", but rather something we "attach" to the explanation built upon "moving electrons".
It's still a property that can't be "touched" without thirst attaching it to ANOTHER entity.
Conversely, "objects in memory" are still precisely the same physical objects (as concepts), merely being "perceived" via a different medium (not eyes, but "inner eyes" of imagination).
On the other hand, "chess-checkers" is an example of breaking this pattern, because it takes the concept of a "chess piece" and then transforms it into the concept of a "checkers piece".
Neither a "chess piece" nor a "checkers piece" is BY ITSELF a physical object (because you can "play" using bottle caps, lol, which are NOT "game pieces"), so it's already step one.
But it takes a much more complex step two to "replace" the already non-physical concept of a "checkers piece" with the equally non-physical concept of a "chess piece".
Now, at SUCH a level - I'm sufficiently convinced that we are finally talking about "abstract NON-physical entities" and intellectual capabilities.
But, fine, help me name it better, if you think that "abstract" starts at a much more "physical" step.