The paper argues that LLM next-token distributions form Markov categories whose paraphrase equivalences can be studied by homotopy theory, but its main theorem is unsupported.
The unreasonable power of the lifting property in elementary mathematics
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abstract
We illustrate the generative power of the lifting property (orthogonality of morphisms in a category) as means of defining natural elementary mathematical concepts by giving a number of examples in various categories, in particular showing that many standard elementary notions of abstract topology can be defined by applying the lifting property to simple morphisms of finite topological spaces. Examples in topology include the notions of: compact, discrete, connected, and totally disconnected spaces, dense image, induced topology, and separation axioms. Examples in algebra include: finite groups being nilpotent, solvable, torsion-free, p-groups, and prime-to-p groups; injective and projective modules; injective, surjective, and split homomorphisms. We include some speculations on the wider significance of this.
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cs.CL 1years
2025 1verdicts
REJECT 1representative citing papers
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A Rose by Any Other Name Would Smell as Sweet: Categorical Homotopy Theory for Large Language Models
The paper argues that LLM next-token distributions form Markov categories whose paraphrase equivalences can be studied by homotopy theory, but its main theorem is unsupported.