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.

I think this is the first highly technical Topos Institute blog post where I walked away and felt like I understood everything I was meant to understand. Heck yeah.

I’ve been thinking about very similar ideas for the better part of a year now; excited to see there’s good work regarding this.

No matter how hard we try to axiomatise mathematics, there will always be strong, independent propositions that don’t need no proofs… but how do we show that a proposition can’t be proven nor disproven?

Nice set of videos on the theory of ordinals and their application to Goldstein sequences.

Ever feel like the mathematics you’re learning doesn’t make any sense to you? Good. In a way, it would’ve been worse if you thought it did make sense.

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).

Horn clauses are a Turing-complete subset of predicate logic. Horn clauses are the logical foundation of Prolog.

see: https://www.metalevel.at/prolog/logic

Very nice introduction to sheaves with bog implications on metascience, cryptography, and economics.

see: https://github.com/DavidJaz/DavidJaz.github.io/blob/master/Talks%2FFRA_2021_David_Jaz_Myers.pdf

The creation of categorical logic has transformed both category theory and logic, blurring the traditional boundary between syntax and semantics and expanding the reach of logic to new application domains and kinds of semantics. Categorical logic offers a unifying, “plug-and-play” toolkit for understanding old logical systems and creating new ones. In this talk, we illustrate this principle through examples of categorical logic drawn from topics such as algebraic theories, bicategories of relations, graphical linear algebra, and statistical modeling.

First Patterson talk I actually understood. Very good lay of the land.

Engineers and category theorists take their analogies very seriously. The many tables seen in this article are regularly referred to in categorical spaces as “Rosetta stones.” The fact that people have found strong connections between classical mechanics and electromagnetism is quite astounding; clearly, differential equations are not to be underestimated.

via: https://www.youtube.com/watch?v=DAGJw7YBy8E

A topic first heavily covered in my learning by Wadler, now reintroduced to by by Baez. Happy to see it has a name.

via: https://www.youtube.com/watch?v=DAGJw7YBy8E

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.

What is infinity? Can there be different sizes of infinity? Surprisingly, the answer is yes. In fact, there are many different ways to make bigger infinite sets. In this video, a few different sets of infinities will be explored, including their surprising differences and even more surprising similarities.

Cantor’s Diagonal Argument proves that there are an uncountable number of real numbers. But what about any interval of real numbers? Are those sets uncountable as well, no matter how small the interval?

Mathematics is based on a foundation of axioms, or assumptions. One of the most important and widely-used set of axioms is called Zermelo-Fraenkel set theory with the Axiom of Choice, or ZFC. These axioms define what a set is, which are fundamental objects in mathematics. And the Axiom of Choice is arguably one of the most important and interesting axioms of ZFC. But what does it really say? And how is it used? This video dives deep into the formal definition of the Axiom of Choice, as well as its important equivalences which have their own fascinating applications in various branches of mathematics. Furthermore, we look into the controversy behind AC, and why it has garnered much discussion throughout its mathematical history.

Curry is a declarative multi-paradigm programming language which combines in a seamless way features from functional programming (nested expressions, higher-order functions, strong typing, lazy evaluation) and logic programming (non-determinism, built-in search, free variables, partial data structures). Compared to the single programming paradigms, Curry provides additional features, like optimal evaluation for logic-oriented computations and flexible, non-deterministic pattern matching with user-defined functions.