I.
Categorical Ontology
A relational ontology grounded in τ and τ³: internal domains, boundary/interface (lemniscate), law/regularity, causation, modality, identity over time, and mereology.
II.
Categorical Phenomenology
Knowledge as sections over covers; justification as gluing constraints; perception/experience as structured mapping; time-consciousness, embodiment, and intersubjectivity.
III.
Categorical Aesthetics
Beauty as invariance and stability; elegance as minimal tension; style/genre as constraints—then applications: golden ratio, fractals, music, visual composition, architecture, and creative refinement.
IV.
Categorical Language
What language adds (and costs); subsymbolic layers; temporalization; self-enrichment; syntax–semantics collapse; reference and pragmatics; translation, drift/repair; public language (law/justice); LLMs and grounding.
V.
Categorical Logic
Scale-sensitive logic (Boolean vs Bayesian), internal randomness, probability as representation, inference as structural necessity, truthmakers, modality, and controlled treatment of contradiction.
VI.
Categorical Ethics
Dignity as a structural invariant; categorical imperative as gluing; fairness/action protocols; ambiguity/monodromy; ethical tests; long-term ethics (animals, future generations) and AI.
VII.
Categorical Societies
Social ontology via spheres/bubbles/foams; scale limits (communities vs cities); architecture as cultural mirroring; generations and drift; capital/networks; overload and fragmentation; coordination at planetary scale.
VIII.
Categorical Mind
Mind as internal topos; self as narrative functor; consciousness as global integration; intentionality and qualia; metacognition and self-awareness; free will as constrained branching; minds vs machines/LLMs; extended mind.
