Categorization is a cognitive shortcut that allows us to group wide varieties of objects and concepts together via a variety of relationships (inherent, temporal, or dependent upon our relationship to the thing).
Categories are a cognitive shortcut. We categorize by appearance, functional equivalence, or some particular categories are conceptually-bound to situations, e.g. “stuff I would take out of the house if it were on fire”. Categories can have any level of granularity. They can have hard or fuzzy boundaries. If they have fuzzy boundaries, there exists prototypes that fit most-fully into any given category. They form hierarchies.
How about this - there is a very fuzzy category we call “Game”. The concept of “game” as a category is an exceptional prototype for “fuzzy categories”.
Categories map to brain tissues. Brain damage has literally caused people to forget what “fruits” are, while retaining the access to “vegetables”.