Token Space: A Category Theory Framework for AI Computations

תקציר מקורי באנגליתarXiv:2404.11624v2 Announce Type: replace-cross Abstract: We introduce the Token Space, a categorical framework for AI computations. A Token is a finite tuple whose entries are elements of a carrier set or symbols of a fixed core; a Token class is a set together with a heap of such Tokens, and Token maps are the functions preserving every Token. The Token Space is built from the category of sets by adjoining identity set categories, forming products and taking a subsets extension. We prove that the resulting categories have all finite limits, finite coproducts and exponentials, but, unlike Set, are not topoi. We then introduce algebraic tokenization: the constants, relations and graphs of operations of a structured set are recorded as Tokens headed by a core symbol. This gives a full and f