I’m investigating the possibility of formally modeling self-referential holons, as described in Poznanski’s Dynamic Organicity Theory and related functional system frameworks, through mathematical structures capable of capturing recursion, transformation, and multiscale dynamics.

Specifically, I’m interested in whether category theory, particularly its higher-order or enriched variants, can be extended or adapted to support functional pathways that:

• Exhibit non-hierarchical recursion
• Encode intentionality or negentropic action
• Support diachronic causality (i.e., where causation is asymmetric and nonlocal across time)

In the Oscillatory Dynamics Transductive-Bridging Theorem (ODTBT), such holons are treated as oscillatory units nested in transductive fields. Their dynamics are governed not just by set-theoretic structure or syntax, but by recursive waveform interactions, expressed through sine-cosine phase modulation across nested scales (the TWIST boundary being the central transductive operator).

My core questions:

• Has category theory been extended to represent functional organization or processual identity rather than static structure?
• Are there frameworks, perhaps in topos theory, process categories, or sheaf theory, that can accommodate self-referential transformations with embedded boundary conditions?
• Could morphisms be reinterpreted as oscillatory transductions, capturing phase-shifted transitions between informational holons?

I'm particularly interested in models that go beyond symbolic logic and can account for functionality as transformation (rather than representation) as the basis of system self-organization.

Any leads on formal approaches, hybrid mathematical structures, or applied category-theoretic models in biology, cognition, or systems neuroscience would be deeply appreciated.