TITLE: What is the name for a function whose codomain and domain are equal?
QUESTION [15 upvotes]: What do we call a function whose domain and co-domain are the same set?
Edit:
While i expressed my question in terms of functions, domains and codomains, i was actually interested in the most abstract mathematical formulation for similar structures. Thus i accepted as the correct answer endomorphism that, being at the level of category theory, answers rather the question: What do we call a morphism from a mathematical object to itself? I could find this out just after getting some answers

REPLY [2 votes]: Another term that is sometimes used, especially in the context of topological spaces and related objects, is "self-map".