The term 'functor' has two common meanings: 1. Function object. In object-oriented languages, it is a feature that allows objects to be used like if they were ordinary functions. 2. A mathematical structure which deals with mappings between categories. This concept is a useful abstraction in some programming languages, notably Haskell, where it is implemented as a type class.

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A functor is a very simple but powerful idea. Category theory is just full of those simple but powerful ideas. A functor is a mapping between categories.