Research in didactics of mathematics has shown the importance that representations have in teaching and learning processes, as well as the complexity of factors related to them. Particularly, one of the central open questions that the use of representations poses is the nature and diversity of objects that carry out the role of representation and of the objects represented. The objective of this article is to show how the notion of semiotic function and mathematics ontology elaborated by the ontosemiotic approach of mathematics knowledge, enables us to face such a problem, by generalizing the notion of representation and by integrating different theoretical notions used to describe mathematics cognition.