Deconstructing the Calculus of Relations with Tape Diagrams
summary
Constructs a concrete diagrammatic syntax — tape diagrams — that embeds ordinary string diagrams inside a second layer and claims a full completeness theorem: the generated axioms are sound and complete for rig categories with finite biproducts and for the positive fragment of Tarski’s calculus of relations. Uses categorical machinery (Rig categories, biproducts, Rel models), an explicit two‑layer grammar and equational axioms, and exhibits worked examples showing union and intersection are represented and the completeness proof succeeds.
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