Kristopher Brown

Research Scientist

Topos US

Kris Brown previously completed a postdoc in computer science at UF and a PhD in chemical engineering at Stanford University. Kris is interested in helping scientists (and others) better organize their knowledge and communicate with each other. Kris studies categorical gadgets such as diagrams, sketches, and (co)limits as a language to construct more transparent, extensible, and composable approaches to problems of scientific interest such as constraint solvers, rewrite systems, linear algebra, and model exploration.

Blog posts

Call for 2026 Summer Research Associates

Come spend the summer at the Topos Institute! For early-career researchers, we’re excited to open up applications for our 2026 Summer Research Associate program.

Kris Brown
2025-11-24

Incremental query updating in adhesive categories

Working in the general setting of adhesive categories, we derive a practical algorithm for incrementally updating a query’s results with respect to small changes in the object being queried.

Kris Brown
2025-08-15

Substitution is also pushout

How we can think about pushouts as applying rules via substitution, featuring examples in categorical databases and Datalog.

Kris Brown
2025-08-06

Taking nonlogical concepts seriously

What is the right math to capture our concepts which don’t have formal definitions? Recent work in philosophy of language clarifies the relationship between logic and good reasoning, with consequences for science, applied math, and AI. In this post we will introduce logical expressivism, its…

Kris Brown
2024-10-11

Responsible mathematics and metaphors of semantics

An exposition of a philosophical argument about how words connect with their meanings, and a tentative connection to work done at Topos.

Kris Brown
2023-12-14

Agent-based modeling via graph rewriting

Rewrite rules are organized via a graphical syntax into discrete-time simulations which can be understood as agent-based models. This representation is transparent, compositional, and serializable.

Kris Brown
2023-07-07

Acsets with variables

Acsets are great, but what if attributes could be variables?

Kris Brown, Kevin Arlin
2023-06-20
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