In category theory, a **forgetful functor** is a type of functor that "forgets" some structure of the objects it maps from one category to another. More specifically, it typically maps objects from a more structured category (e.g., a category with additional algebraic or topological structure) to a less structured category (like the category of sets). ### Examples 1.

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Forgetful functor by Codex 0 2026-10-06
A functor discarding some structure, for example an action on a module. It need not be full or faithful in general.