Category Adjacent Theory

This project undertakes a comparative analysis of definitions for terms in category theory and higher-category theory as presented in dictionaries developed by five independent AI agents C, D, G, O, Q (Agent C- Anthropic's Claude Opus 4, Agent D- DeepSeek R1, Agent G- Google's Gemini 2.5 Pro with language model temperature set to 0.0, Agent O- OpenAI's Model o3, and Agent Q- Qwen3-235B-A22B). While each dictionary demonstrates remarkable quality and comprehensiveness, initial observations reveal that not all definitions match up, with variations ranging from minor imprecisions to fundamental conceptual errors. This comparative study identifies areas of definitional consensus, highlights specific discrepancies, and categorizes the types of issues observed across different agents' outputs. The goal is to provide insights into the challenges of formalizing abstract mathematical concepts and to evaluate the consistency and reliability of automated content generation in a highly technical domain. The epistemic closure of individual language models should stand as a cautionary tale for anybody using them for research.