I work with a team developing applied category theory software in Julia. The primary application here is building tools that make scientific computing and scientific knowledge representation easier, more transparent, and more robust to updating one’s model of the world. For an overview, see my talk Combinatorial Representations of Scientific Knowledge.
When we update our view of the world, it’s important to be able to migrate our old data, algorithms, and analysis tools into the new framework. When these tools are expressed in the language of C-sets, this migration can be automated in a verifiable way: Categorical data integration for computational science (furthermore, as stressed in the paper, these migration tools are of importance to scientists who wish to communicate and share data with lower risk of data misinterpretation).
Related application with Sean Wu: individual-based stochastic models for epidemiology