The article analyzes the state of informatization of processes and phenomena in modern institutions of higher education. The main conceptual provisions of modeling of processes and phenomena of higher education institutions are offered in the work. Models of correspondence of options of interaction of units of providing higher education institutions and procedures of formalization technology, models of educational and methodical providing, models of digital platforms of knowledge of institutions of higher education and models of procedures of interaction of elements of management of institutions of higher education by methods of category theory are developed. Methods of systems analysis, mathematical logic, category theory, heuristic methods were used to build models. The results were obtained. The problem is formulated, which is to unite the positive aspects of existing and existing information technologies, as well as the elimination of negative aspects that hinder the processes of information integration and the development of intellectual rules for interaction. Developed an example of formalization, in our opinion, the most complex and most important for the university educational and methodological support, abstracting from most types of support. Schematic solutions, as well as experience in organizing student learning based on the support system of educational processes were shown using models of disciplines and professional knowledge of students, as well as by combining them in one specialty, called digital platform of professional knowledge. A metamodel of a higher level of generalization has been developed, which allows its use in modeling other types of software. It is characterized by the complexity of relations between participants in the learning process, on the one hand, standardization and strict requirements for learning processes on the other hand, which led to the construction of learning processes in the language of theory of categories and functions. Formalization of learning processes in a more abstract language allowed to develop this metamodel. The development of the basis for the knowledge base of the intelligent system "Smart Institution of Higher Education" will solve a wide range of tasks at different levels of the hierarchy of management, control, monitoring, scheduling processes and phenomena in higher education institutions.