Narrative structure (story functor)

Narrative structure is τ-categorically the *Story Functor*: a functor St : Episodes → M_τ that maps lived episodes (events, encounters, decisions) into the agent's Mind-Topos with self-relevance, plus a coherent natural transformation between Story Functors over time. Narrative identity (VII.T40) is exactly: an agent persists as a self when there exists a coherent natural transformation between successive Story Functors.

Categorical invariant. St : Episodes → M_τ — functor mapping experiences to mind-topos-internal images with self-relevance index. Narrative identity = ∃ coherent natural transformation η : St_t ⇒ St_{t+Δ}; growth = η is non-trivial (revision); pathology = η fails to exist (dissociation).

Primary registry anchor: VII.T40

Supporting items: VII.D83, VII.T39, VII.D82

1. I.K0 — Universe Postulate
2. VII.D82 — Mind as Internal Topos
3. VII.T39 — Mind-Topos Structure Theorem
4. VII.D83 — Story Functor — episodes to mind-topos with self-relevance
5. VII.T40 — Narrative Identity as Functor — identity persists when coherent natural transformation exists

Lean modules referenced: TauLib.BookVII.Logos.Sector

Narrative structure is instantiated whenever a sequence of episodes is integrated into a self-referential trajectory — autobiographical memory, life-stage transitions, growth-through-crisis, the felt continuity of selfhood across time. Failures of narrative coherence (amnesia, dissociation, profound trauma) are exactly failures of the natural transformation η between Story Functors.

Examples:

• Autobiographical memory — episodes mapped via St with self-relevance index, glued into one trajectory
• Bildungsroman / coming-of-age — non-trivial η encodes growth through revision (VII.T40)
• Trauma narrative repair — therapeutic re-narration restores η that crisis disrupted
• Late-life integrity (Erikson) — narrative coherence as global section across the life-span

Register codomain: Reg_E reads the empirical episode-trace (memory, behavioral continuity); Reg_C reads the stance-component (identification: 'this is my story'). Narrative identity is a multi-register coupling, with Reg_C carrying its non-reductive core.

Manuscript reference: manuscript-sources/book-07/part09/ch107.tex

Status: Formalized

Module: TauLib.BookVII.Logos.Sector

Lean kind: theorem

Lean symbol: Tau.BookVII.Logos.Sector.narrative_identity

Related glossary entries

• MG-H03-mind-topos Mind-Topos Structure
• MG-H04-subjectivity Subjectivity (first-person perspective)
• MG-H11-self-recognition Self-Recognition (E₃ operator)

Referenced by

• MG-H11-self-recognition Self-Recognition (E₃ operator)