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Blockchains are formal systems for equipping objects with value, transacting their exchange, and creating domain-specific event histories. Categorical cryptoeconomics is the application of category-theoretic methods to blockchain study with formalisms which pertain to blockchains and generalize to the programmable computational infrastructure more...
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... progression of higher categorical cryptoeconomic ideas are introduced: HoTT (homotopy type theory) blockchains, Petri net computad ledgers, coregulator DAOs (decentralized autonomous organizations), and cohomology ZKPs (zero-knowledge proofs) ( Table 3). The progression is first nodes that themselves are equipped with additional structure (e.g. ...Citations
... The method is widely used in science (physics, chemistry, biology) [Spivak, 2014] as many complex systems can be represented with the same functorial logic [Baez, 2023]. Another benefit of diagrammatic reasoning is computability. ...
A category theory perspective is taken as an abstraction technique to lift domains to higher structures of interrelation. Categorical Cryptoeconomics unifies category-theoretic approaches in blockchain, finance, accounting, and economics aimed at real-world asset digitization, global risk management, and AI-quantum transition. Categorical Smart Network Field Theory joins categorical smart network treatments (in blockchain, AI, and quantum) with categorical field theory. HoTT Blockchains (homotopy type theory) are the idea of instantiating blockchains as same-shape logic elements for secure computability, formal verification, and interoperability. The result of Categorical Cryptoeconomics and Categorical Smart Network Field Theory is the formalization of digital trust to support an era of AI math agents, experiential self-learners, robots, and autonomous vehicles.
... The method is widely used in science (physics, chemistry, biology) [Spivak, 2014] as many complex systems can be represented with the same functorial logic [Baez, 2023]. Another benefit of diagrammatic reasoning is computability. ...
We discuss blockchain formal methods and propose category theory as the mathematics of the smart network stack and valuation in the DeFi economy. Financial markets are expanding into blockchain, AI, and quantum technologies, including crypto derivatives and DeFi protocols. Beyond finance, blockchains provide a foundational protocol layer for scientific advancement and human-compute interaction as token-propelled AI agents may undertake actions on our behalf. Category theory offers a flexible framework to formalize the mathematics of our smart network futures introduced here as Categorical Cryptoeconomics.
