Vignettes

FunctorFlow.jl ships a set of longer worked examples that sit between a quick start and the API reference. These pages are published with the docs site, so the links below open the rendered HTML or PDF artifacts directly from gh-pages.

Core walkthroughs

01 Getting Started - first steps with the package and diagram authoring. Julia HTML | PDF | Python HTML
02 DSL Macros - macro-based diagram construction and notation. Julia HTML | PDF | Python HTML
03 Kan Extensions - left and right Kan extensions in executable form. Julia HTML | PDF | Python HTML
04 Block Library - reusable building blocks for common diagram patterns. Julia HTML | PDF | Python HTML
05 Composition - composing larger systems from smaller categorical pieces. Julia HTML | PDF | Python HTML
06 Obstruction Loss - constraint-style losses for structural guidance. Julia HTML | PDF | Python HTML
07 Lux Neural Backend - compiling diagrams into trainable Lux models, including dedicated CATAGI backends for TopoCoend, horn filling, and bisimulation quotienting. Julia HTML | PDF | Python HTML

Categorical extensions

08 Universal Constructions - products, coproducts, pullbacks, and pushouts in practice. Julia HTML | PDF
09 Causal Semantics - categorical views of interventions and causal structure. Julia HTML | PDF
10 Topos Foundations - internal logic and topos-flavored foundations for the DSL. Julia HTML | PDF
11 Canonical V1 Example - a consolidated end-to-end example aligned with the V1 roadmap. Julia HTML | PDF
12 Sudoku Constraints - using diagrams and losses for structured discrete reasoning. Julia HTML | PDF
13 Predict-Detach - predictive objectives with detach-style training structure. Julia HTML | PDF

World models and neurosymbolic systems

14 JEPA World Models - diagrammatic world-model objectives inspired by JEPA. Julia HTML | PDF
15 KET Language Model - categorical sequence modeling and KET-style constructions. Julia HTML | PDF
16 Kan Duality - dual Kan constructions and their modeling consequences. Julia HTML | PDF
17 Causal JEPA - combining causal structure with JEPA-style objectives. Julia HTML | PDF
18 Neurosymbolic Pipelines - larger mixed symbolic-neural workflows built from diagrams. Julia HTML | PDF
22 Democritus Assembly - local causal graph gluing, repaired global sections, and regrounding back to fragments. Julia HTML | PDF
23 TopoCoend Triage - inferred latent covers over clinical signals before Kan aggregation into context-level risk summaries. Julia HTML | PDF
24 Bisimulation Quotient - paired latent controllers, declared bisimulations, and coequalizer-based behavioral abstraction. Julia HTML | PDF

For the CATAGI-oriented material, the most coherent reading path is:

18 Neurosymbolic Pipelines for the full symbolic overview.
23 TopoCoend Triage for learned-cover aggregation in a focused example.
24 Bisimulation Quotient for coequalizer-based behavioral abstraction.
07 Lux Neural Backend for the trainable Lux counterparts.

V1 parity demos

19 Temporal Repair and Schrodinger Bridges - persistent-world repair, compilation, and bridge summaries for the v1 temporal stack. Julia HTML | PDF
20 Red-Wine Categorical DB Bridge - repo-local categorical database pullback, pushout, and truth-witness materialization on the red-wine sample study. Julia HTML | PDF
21 TCC Method Pullback - DID-vs-IV pullback materialization and compilation against the Democritus causal-claims corpus. Julia HTML | PDF

CLIFF orchestration demos

25 CLIFF Route Runtime - build a runnable routed executor in Julia, drive convergence-aware stopping, and compile the resulting route artifact. Julia HTML | Markdown
26 CLIFF Interactive Routing - execute a checkpointed Democritus-style route, inspect its shared broadcasts, and compile the paused route result. Julia HTML | Markdown