Acyclic Networks: Causal Comparisons, Convex Minors, and Gauge Descent
Source: hexagonmath.org/abs/2611.00122v1
We study natural transformations, minors, and symmetric monoidal decorations of finite directed acyclic networks. For any weakly connected small source category, a natural transformation into a free acyclic path category is determined by one component. If more than one transformation exists, common prefixes and suffixes give a canonical factorization through two constant functors and identify the transformation set with a single set of directed paths. Consequences include boundary rigidity, a decision algorithm, and a fundamental-group obstruction to non-uniqueness. For fusion–embedding…
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