category

The traditional way of describing the similarities and differences between constituents is to say that they belong to categories of various types. Thus, words like boy, girl, man, woman, etc. are traditionally said to belong to the category of Nouns, whereas words like a, the, this, and that are traditionally said to belong to the category of Determiners.

The use of the word ‘factor’ shows the explicit intention of categorists to work with functions in an algebraic manner: a category is an algebra of functions.