Starting from the modeling relation, as introduced by the late Robert Rosen, we propose a relational method for studying impredicative systems, which are natural systems that have models containing hierarchical cycles. The general theory of impredicative systems vastly generalizes autopoietic systems, and has implications in the biological, psychological, and social realms, from which we offer many exemplifications. The method is formulated in category theory in terms of alternate descriptions and their functorial connections.
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