An endofunctor is a functor that maps a category to itself, meaning it takes objects and morphisms from one category and produces new objects and morphisms within the same category. This concept is fundamental in category theory as it allows for the manipulation of structures within a single category, making it possible to define concepts like monads, which are built upon endofunctors. Endofunctors are crucial in understanding how transformations operate within the same category, facilitating the construction of more complex structures.
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