A nice walk from homotopy to Lie theory to category theory to combinatorics.

Can’t fully understand because there are no words, but the author looks to be making a very neat connection between coalgebras and the executions (here “traces”) of transition systems. Became aware of her work through Adjoint School 2026.

via: https://www.cs.uni-salzburg.at/~anas/talks.html

Scientists and engineers like to describe processes or systems made of smaller pieces using diagrams: flow charts, Petri nets, electrical circuit diagrams, signal-flow graphs, chemical reaction networks, Feynman diagrams and the like.   Many of these diagrams fit into a common framework: the mathematics of symmetric monoidal categories.  When we embrace this realization, we start seeing connections between seemingly different subjects.  We also get better tools for understanding open systems: systems that interact with their environment.  This takes us beyond the old scientific paradigm that emphasizes closed systems.

Going down the categorical systems theory rabbit hole; very good exposition from Baez as per usual. I also finally know what a monoidal category is, so that’s pretty handy. I ought to read the paper this talk is based on at some point.

see: https://math.ucr.edu/home/baez/rosetta/

via: https://en.wikipedia.org/wiki/Monoidal_category

Acsets are a novel infrastructure for handling data of different shapes, based on category theory and implemented in Catlab.jl. Acsets generalize both graphs and dataframes, and allow a much more general approach to data manipulation than was previously available. We will discuss both the mathematics of acsets and some of the metaprogramming techniques we used to implement them in Julia. Finally, we will give examples of how acsets have been key in developing many projects in AlgebraicJulia.

Probably the best AlgebraicJulia tutorial on the planet LOL.

Great pair of talks.

via: https://golem.ph.utexas.edu/category/2025/10/a_complex_qutrit_inside_an_oct.html

A now classic talk that links propositions, types and categories together.

Today we have thousands of apps to choose from, but it’s difficult to craft our own custom tools that do exactly what we need. Geoffrey Litt’s research explores malleable software: approaching software that feels more like a Lego set that anyone can combine to create their own tools, without programming. This talk will feature demonstrations of malleable software tools developed in contexts from travel planning to collaborative writing. It will also discuss how AI might enable a Cambrian explosion of custom tools created by non-programmers, and what kinds of new software environments will be needed to take advantage of that new power.

Great overview of Geoffrey’s work over the past few years and how LLMs could fit into the future of end-user programming.