$$ $$ Category theory often sheds light on old problems by redescribing them in a conceptually cleaner way, but it less frequently gets used to develop concrete algorithms for practical problems. In this post, the problem we address involves a query we care about: we want to maintain the answer set to some query (e.g. “how many paths of length two are there in this graph?”) when the thing being queried is changing frequently. If the changes are frequent enough, we don’t want to have to...| Topos Institute
How we can think about pushouts as applying rules via substitution, featuring examples in categorical databases and Datalog.| Topos Institute
Nate Osgood, together with 4 students from the Computational Epidemiology and Public Health Informatics Lab in Saskatoon, Canada, recently ran a community group model building event focusing on the drivers for homelessness in their city. This post describes the event, and the next steps that they are planning to take.| Topos Institute
In this blog post, I’ll reformulate Ingo Blechschmidt’s “synthetic quasi-coherence” axiom — or more precisely his “general nullstellensatz” — as a lifting property inspired by Ivan Di Liberti’s work on coherent toposes and ultrastructures. This lifting property shows that synthetic quasi-coherence can be derived from a sort of “directed path induction” for toposes, suggesting the possibility of an internal logic for all toposes in which the axioms for any sort of synthet...| Topos Institute
Another year, another cohort of wonderful Summer Research Associates (RAs) at Topos working on exciting projects. As is now the custom, we’ve asked each of them to introduce themselves and write a little bit about what they’ll be working on over the summer, with more detailed blog posts from each one to come soon!| Topos Institute
This is the second part in a series about diagrammatic reasoning, inspired by e-graphs. Last time, we reviewed the concept of initial functor and showed by example how to calculate with diagrams and initial functors. This time, we make that calculus more systematic and we reconceive e-graphs in terms of initial functors. 1 Weak equivalence of diagrams We’ve been deriving equations by chaining together initial functors between diagrams, going in either direction. Let’s give a name to this ...| Topos Institute