Volume 15 — Observer Categories and Collapse Functors
Category Theory of Golden-Base Systems
This volume recasts the entire collapse framework in category-theoretic terms. Traces become morphisms, observers become objects, and the golden constraint becomes a fundamental categorical property.
Chapter Index
Chapter 240: CollapseCat
Category of Collapse Paths and Trace Morphisms
The fundamental category of collapse structures.
Chapter 241: ObsFunctor
Functorial Mapping Between Observer Contexts
Functors between observer categories.
Chapter 242: NatTransform
Natural Transformations of Observer-Driven Collapse Views
Natural transformations in trace space.
Chapter 243: CollapseLimit
Limits and Colimits over Collapse Trace Cones
Universal constructions in collapse categories.
Chapter 244: ObsObject
Observer Nodes as Objects in Collapse Categories
Observers as categorical objects.
Chapter 245: CollapseCone
Construction of Collapse Cones and Co-Cones
Cone constructions for limits.
Chapter 246: CollapseCommute
Commutativity Conditions in Collapse Category Diagrams
When trace paths commute.
Chapter 247: PreserveFunctor
Collapse Structure Preserving Functors
Functors maintaining φ-constraint.
Chapter 248: TraceFactor
Factorization of Collapse Paths Through Category Objects
Unique factorization in categories.
Chapter 249: CollapseYoneda
φ-Collapse Reformulation of Yoneda Embedding
Yoneda lemma for trace categories.
Chapter 250: CollapseEnrich
Enriched Categories from Collapse Tensor Properties
Enrichment over trace tensor categories.
Chapter 251: ObsIndexCat
Index Categories of Observer-Specific Collapse Access
Indexed category constructions.
Chapter 252: CollapseAdjoint
Collapse Adjoint Pairs and Dual Observer Views
Adjunctions in collapse theory.
Chapter 253: TensorFib
Collapse Tensor Fibrations and Lifting Conditions
Fibration structures in trace space.
Chapter 254: CollapseMonoidal
Collapse-Aware Monoidal Structures over Observer Systems
Monoidal categories with trace tensor.
Chapter 255: InternalLogic
Observer Internal Logic as Collapse-Aware Category Theory
Logic internal to categories.
Key Concepts Introduced
- Collapse Categories: Traces as morphisms
- Observer Functors: Perspective mappings
- Natural Transformations: Structure preservation
- Categorical Limits: Universal properties
- Yoneda Embedding: Representability
- Adjoint Pairs: Dual perspectives
Dependencies
- Volume 3: Algebraic structures
- Volume 6: Logic foundations
- Volume 7: Observer theory
Next Steps
- Volume 16: Graph categories
- Volume 21: AGI categories
- Volume 31: Reality categories
"In categories, collapse finds its truest form."