Is Category Theory Being Co-opted?

Is category theory being co-opted? These authors think so:

• Esteban Montero and Brandon Baylor, Category theory is being co-opted, Holon Substack, 7 September 2025.

Category theory offers a powerful new way of viewing the world… if we embrace its lessons and are willing to think in brand new ways. But what are the chances of that? It could easily become just another way for the rich and powerful to get more rich and powerful while the world burns. Applied category theory is already heavily funded by the military and tech firms.

Luckily, the UK has injected money into category theory for developing safeguards to AI. It’s risky, but it might do some good. And some of us are using category theory to develop new software for epidemiology, and soon labor economics, trying to model aspects of the green transition.

Montero and Baylor’s article is interesting—but it ignores those initiatives. It focuses heavily on the supposed ills of set theory—but I don’t think escaping set theory is either necessary or sufficient to free up our ways of thinking.

I have plenty of other complaints about this essay:

• Much as I like applied category theory, I don’t think our work so far “demonstrates the immense practical power of categorical thinking.” I think the jury is still out, which is why I keep working hard on this.

• The focus on Buddhism makes me uneasy. Buddhism has some good ideas, but I don’t think the cause of good new mathematics should be shackled to this religion.

• It seems like a bad idea, tactically, to combine this sort of essay with a plea for funding—even if you really want funding!

Nonetheless, not enough people are talking about the remarkable transformation of category theory into an ever-more-practical discipline, and the question of whether it will be truly revolutionary, or just another tool.

So until someone writes a better essay about this, it’s worth reading this one!

I particularly like their vision of how categorical network theory could be part of a new civilization:

• Systems Engineering: For a systems engineer designing a smart grid, a logistics network, or a complex software architecture, the most important thing is not the individual components, but the rules of their interaction. Category theory provides a formal language for designing systems not by specifying parts, but by defining relationships, interfaces, and compositions.

• Ecological Thinking: In ecology, an organism cannot be understood apart from its niche—the web of relationships it has with its environment and other organisms. The categorical perspective aligns with this systemic view, seeing entities as defined by their context.

• A New Civilization: At the largest scale, this relational philosophy suggests a different way of organizing society. Instead of a collection of atomized individuals, it envisions a system of interconnected stakeholders, where the health of the whole is determined by the quality of the relationships between the parts.

We just need to work out a few details.