Rethinking AI: From Functions to Functors

Abstract

We propose a new theoretical foundation for artificial intelligence (AI) and machine learning (ML), building on ideas in pure mathematics relating to categories and functors. This paper builds on our AAAI 2025 tutorial Thinking with Functors: Category Theory for A(G)I, which provides background material. In addition, our recent papers on intuitionistic j-do calculus in Topos Causal Models} and GAIA: Categorical Foundations of Generative AI, illustrate how to generalize well-known formalisms in AI, such as causal inference and deep learning, to a category-theoretic setting.