nLab
endofunction

Contents

Idea

An endofunction (or self-mapping or other variation) is an endomorphism in the category of sets, that is a function from a set XX to XX itself. This is the typical meaning of the word ‘function’ in some contexts, such as high-school algebra (where XX is the set of real numbers, although there we actually use partial functions) or when distinguishing from the higher-order concepts of functional and operator.