This paper focuses on the topic of intentionality, which is the power of the mind to be directed towards some object or state of affairs. Intentionality structures the (inter) subjective side of experience, traditionally explored by Edmund Husserl's phenomenology. I intend to introduce the basics of a semiotic interpretation of phenomenological intentionality with the undertaking of realistically grounding it, going beyond the alternative approaches of Modern transcendentalism and the contemporary trend to re-orient phenomenology naturalistically excluding the foundational perspective. This is possible in virtue of a relational reading of phenomenological ontology, where the theoretical core is the following: a sign-driven synthesis of the object, occurring within the onto-logical sphere of the signification processes (semeiosis), and hence outside the epistemological sphere of the subjective self-consciousness. Based on a fragmentary suggestion detectable in the early phenomenological work of the German phenomenologist Max Scheler, the proposed interpretation aims at strengthening the traditional (inter) subjective approach of phenomenology to the categorial study with the "in the third person" objective approach distinctive of semiotics, sharing in principle with the former a common pre-logical and hence ante-predicative level of enquiry. Mathematical Category Theory provides a rigorous framework in developing this unification step, because it deals with relational structures (relational categories) underpinning the predicative ones.