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

This is the kind of mathematics I was put on this earth to do. The equation explorer is also just a genuinely useful tool for looking up equations; did so earlier this year as part of preparations for a lecture I gave.

When you hear that someone is “studying algebra”. What comes to mind? Are they drilling through thousands of factorisation problems? Are they an undergraduate student of mathematics, pursuing studies you can’t think of any real-world applications for? Well, you’re all wrong (or maybe you’re not).

This blog post provides an overview of the work I had done with José Siqueira this summer. Inspired by the free Boolean/Heyting algebra of a given set, we develop a free-forgetful adjunction between posets and PLTL temporal algebras, where PLTL denotes propositional linear temporal logic. We provide a description of their induced Eilenberg-Moore categories. We describe how this could be used to temporalise systems and logics through hyperdoctrines and connect this to the stream comonad. We end with future research directions, connecting this topic with the cofree comonad of polynomial functors and temporalising doxastic logic.

The logic algebra stuff was neat. Got lost in the cat sauce as per usual LOL.