A book divided in several chapters/topics, can also be considered to be divided in categories (or have categories)?
Not sure if category can be used in this case, or if it should only be used in the context of category theory.
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Books can be sorted or put in categories. For example, a book about Philippine cuisine written by Dostoyevski could be sorted into the categories "Cooking", "Russian author", "Philippines". But it would be sorted into each of these categories as a whole. You can't divide the book into categories. A category is a superordinate concept, while chapters is a subordinate one.
A catalog is a type of book that can have categories. The categories may be related to the book as a whole and have no relation to each other, or they may be related to each other using categories to delineate between subtleties.
Reference books, in general, and especially repair manuals, have categories.
I can imagine a book entitled "The Usage of English Around the World" having categories based on geography or history or any other method one may choose for categorizing how English is used throughout the world.
I can also imagine someone writing an autobiographical book having a category consisting of poetry they've written, another category for personal correspondence, another for diary entries, and another with newspaper clippings about them. Taken separately they do not provide a complete picture of the author's life, but taken together you could get a better understanding than with narrative alone.