Used to classify things into broad types or groups, often with a sense of belonging to a certain kind.
He falls into the category of excellent people.
His work ranks among the best.
This problem belongs to the difficult category.
This fish belongs to the category of high-grade fish.
I divided the books into categories according to their content.
分類 refers to the act of classifying things, whereas 部類 refers to the resulting category or class itself.
カテゴリー is a casual loanword for 'category', while 部類 is a more literary, native-Japanese term with a similar meaning.
部類 refers to a specific class or category within a larger group, while 類 is a broader, more general term for kind or sort.
Compound of 部 (section, division) and 類 (kind, sort). The exact historical derivation is uncertain, but the combination naturally yields the meaning 'class' or 'category'.