How does the brain process generalizations? What is the current thinking on how the brain processes generalizations? For example, the abstract idea of a right angled triangle vs specific instances of right angled triangles? Or the general idea of a cat vs specific instance of cats?

How does a generalization live in the brain? What's the current thinking on how it is encoded?

Medieval philosophers point to such abstractions (that are not material timeless "things") to argue that something itself not material and timeless must exist to "sense" them i.e. a soul. Which is hogwash. But how does one state the nature of such things in terms of human cognition? What is going on when we consider such abstractions?
The thing that comes to mind first are the Gestalt principles. Up front -  the Gestalt theory of perception has been criticized as being a descriptive theory, and not providing much insight into the processes that lead to perception.

However, the principles do address your question, as the Gestalt theory dictates that humans visually and psychologically attempt to make order out of chaos, to create harmony or structure from seemingly disconnected bits of information. Much of the principles deal with figure/ground separation, but an important other aspect is similarity, and specifically


  Gestalt theory states that things which share visual characteristics
  such as shape, size, color, texture, or value will be seen as
  belonging together in the viewer’s mind.


The principle of grouping (Quinn et al., 2002) is indeed fundamental here:


  The similarity principle claims that elements tend to be integrated into groups if they are similar to each other.


Reference
- Quinn et al, Psych Sci (2002); 13(4)