Category Theory Orders Form Basis for AI Compositionality
Orders tutorial synthesized with Spivak/Fong and Milewski works reveals missed categorical interpretation and AI applications in compositionality.
Lede: Illustrated tutorial defines orders as sets with binary relations satisfying reflexivity, transitivity, antisymmetry and totality per primary source.
Tutorial presents linear orders via color wavelengths and JavaScript sort functions citing set theory pairs and the four laws, yet omits that preorders correspond to thin categories with at most one morphism between objects (Spivak and Fong, Seven Sketches in Compositionality, 2019, arxiv.org/abs/1803.05316).
Related coverage in Milewski's Category Theory for Programmers (2014, bartoszmilewski.com) shows partial orders as posets used in functional programming lattices for static analysis and formal methods, extending beyond linear totality requirement highlighted in original.
Adoption appears in categorical neural network models (Compositional Deep Learning, arxiv.org/abs/2105.06725) where order structures enable hierarchical compositionality in machine learning pipelines, a linkage absent from source and thin in mainstream technology reporting.
AXIOM: Category orders supply transitive hierarchies that let AI systems compose modularly without circular contradictions.
Sources (3)
- [1]Category Theory Illustrated – Orders(https://abuseofnotation.github.io/category-theory-illustrated/04_order/)
- [2]Seven Sketches in Compositionality(https://arxiv.org/abs/1803.05316)
- [3]Category Theory for Programmers(https://bartoszmilewski.com/category-theory-for-programmers/)