Categorical computing is an emerging scientific approach that leverages the many constructs from the edifice of category theory into practical computation. This mini-course introduces participants to the foundations of this approach using the Julia package Catlab, a powerful open-source tool for working with categories, graphs, and algebraic structures in a computational setting. The course will provide an accessible entry point for those interested in exploring how categorical methods can be implemented and applied in research and modeling.

The sessions will guide attendees through the central ideas of categorical computing, highlighting how concepts such as schemas, C-sets, functors, natural transformations, and universal constructions—including products, coproducts, pushouts, and pullbacks—as well as constructions such as structured cospans, operads, and the category of elements can be used to build and analyze models. By combining theory with hands-on use, and by guiding participants to the growing number of projects in the AlgebraicJulia ecosystem based around Catlab, participants will see how categorical tools provide flexible and general abstractions for computing, and connect abstract mathematics to real-world applications in areas such as systems modeling, engineering, and data science.  

This mini-course is designed for graduate students, early-career researchers, and professionals seeking to broaden their toolkit with a novel scientific approach. No prior experience with category theory, categorical computing or Julia is required. The course will provide both conceptual grounding and practical examples. Attendees will leave with a deeper understanding of how category theory can shape and support abstractions for practical computation, and with skills to explore its potential in their own domains of interest.

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Learning Objective: This mini-course fulfills the first objective by initiating attendees into categorical computing, a fast-maturing scientific framework that brings category theory into practical computation, including with visual support in a Jupyter notebook-based interactive environments. While category theory is widely used in mathematics, its computational use in domains such as engineering and dynamic modeling—via implemented software tools like the Julia package Catlab—remains new and not yet widely recognized. By offering a structured and approachable introduction, the course will lower the entry barrier to this emerging, rapidly developing, and high-potential area, broaden its audience beyond specialists, and extend its appeal to both researchers and students from diverse backgrounds.