The term of a “process” is used in Software Engineering (SE) theories and practices in many different ways, which cause confusion. In this paper we give a more formal description a Process-Ontological Model which can be used to analyze some problematic nature of software engineering. Firstly we present a process ontology in which everything is in a process. There are two kinds of processes: “eternal” and actual, where actual processes are divided into physical and mental processes. Secondly, we propose a topological model T for actual processes. Thirdly we propose an algebraic model for eternal processes, i.e. concepts. Lastly, by using category theory we connect these two models of processes together in order to get a category theoretical description of the Process-Ontological Model. That model is a functor category CO(T)op, i.e. the category of presheaves of concepts on T. Moreover, by using the Yoneda embedding we can represent the Process-Ontological Model as certain “structured sets”, and all of their “homomorphisms”.
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