sub-category

noun
  1. 1

    With respect to a given category, a more narrow category.

  2. 2

    A subclass of a category which is itself a category, whose arrows are a restriction of the arrows of the parent category, and whose composition rule is a restriction of the parent category's

Source: https://en.wiktionary.org/wiki/sub-category, https://en.wiktionary.org/wiki/subcategory