Tull, SeanSeanTullKleiner, JohannesJohannesKleiner0000-0002-2197-8898Smithe, Toby St ClereToby St ClereSmithe2025-01-072025-01-072023https://fis.uni-bamberg.de/handle/uniba/105583We present a categorical formulation of the cognitive frameworks of Predictive Processing and Active Inference, expressed in terms of string diagrams interpreted in a monoidal category with copying and discarding. This includes diagrammatic accounts of generative models, Bayesian updating, perception, planning, active inference, and free energy. In particular we present a diagrammatic derivation of the formula for active inference via free energy minimisation, and establish a compositionality property for free energy, allowing free energy to be applied at all levels of an agent's generative model. Aside from aiming to provide a helpful graphical language for those familiar with active inference, we conversely hope that this article may provide a concise formulation and introduction to the framework.engString Diagrams370preprint10.48550/arxiv.2308.008612308.00861