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The paper is concerned with modelling distributed systems by specifying their states and processes. Processes are defined as activities in a universe of objects, each object with a set of possible internal states, each activity changing states of some objects and establishing or destroying relations among objects. Partial operations of composing processes sequenially and in parallel are defined. It is shown that certain sets of processes form together with these operations categories with additional structures and special properties, that processes of a system can be represented as morphisms of such categories, and that independence of processes can be characterized in a natural, purely algebraic way.