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Autopoiesis as viability-localized self-production in a topos
1Universidad Andres Bello (UNAB), Escuela de Ciencias de la Tierra, Facultad de Ingenieria, Republica 220, Santiago, Chile.
Bio Systems
|May 10, 2026
Summary
This study defines autopoiesis using topos theory, modeling living systems as self-maintaining networks. The research introduces four axioms for autopoietic systems, with applications to cellular sheaves and tissue organization.
Area of Science:
- Theoretical Biology
- Mathematical Biology
- Category Theory
Background:
- Autopoiesis describes living systems' self-production and maintenance.
- Existing definitions lack a formal mathematical framework for closure and boundary conditions.
- Topos theory offers a powerful language for modeling complex organizational structures.
Purpose of the Study:
- To develop a rigorous topos-theoretic definition of autopoiesis.
- To formalize the concepts of viability, production, repair, and boundary maintenance.
- To establish axioms defining autopoietic systems and explore their implications.
Main Methods:
- Utilizing Lawvere-Tierney topologies for viability.
- Employing monads to model production and repair processes.
- Defining boundary maintenance through specific maps and predicates.
- Formulating four axioms (AP1-AP4) for autopoietic systems.
Main Results:
- A novel topos-theoretic definition of autopoiesis is proposed.
- Four axioms governing autopoietic systems are established, including viability-local closure and constraint-respecting production.
- The framework is applied to cellular sheaves over finite tissues, simplifying closure tests.
Conclusions:
- The topos-theoretic approach provides a robust mathematical foundation for autopoiesis.
- The proposed axioms offer a precise characterization of living organization.
- Applications to cellular structures reveal local-to-global obstruction signals in loopy tissues.
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