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A computer system is said to be algebraic if it contains discrete controllable post-silicon nodes. A theoretical-categorical approach to the design of such systems is proposed, aimed at the effective application of mathematical methods for mapping computational problems on the architecture of such systems. Categories are constructed whose objects are the algebraic models of computing nodes and systems, and the morphisms are the specifications of the actions for integrating nodes into systems. The final diagrams in such categories are formal architectural models of algebraic computing systems.