Position: LLMs Must Use Functor-Based and RAG-Driven Bias Mitigation for Fairness

Biases in large language models (LLMs) often manifest as systematic distortions in associations between demographic attributes and professional or social roles, reinforcing harmful stereotypes across gender, ethnicity, and geography. This position paper advocates for addressing demographic and gender biases in LLMs through a dual-pronged methodology, integrating category-theoretic transformations and retrieval-augmented generation (RAG). Category theory provides a rigorous, structure-preserving mathematical framework that maps biased semantic domains to unbiased canonical forms via functors, ensuring bias elimination while preserving semantic integrity. Complementing this, RAG dynamically injects diverse, up-to-date external knowledge during inference, directly countering ingrained biases within model parameters. By combining structural debiasing through functor-based mappings and contextual grounding via RAG, we outline a comprehensive framework capable of delivering equitable and fair model outputs. Our synthesis of the current literature validates the efficacy of each approach individually, while addressing potential critiques demonstrates the robustness of this integrated strategy. Ensuring fairness in LLMs, therefore, demands both the mathematical rigor of category-theoretic transformations and the adaptability of retrieval augmentation.