endofunctor
A functor from a category to itself. Rare technical term used in category theory and functional programming.
An endofunctor is a functor from a category to itself in category theory.
関手 (functor) is the general term; 自己関手 specifically refers to a functor whose source and target categories are the same.
Compound of 自己 (self) and 関手 (functor), a calque from English 'endofunctor'.