Realising a world where the systems that surround us benefit us all| Topos Institute
An e-graph, short for “equality graph,” is a data structure that maintains a congruence relation on expression trees: an equivalence relation stable under forming new expressions. First devised by Nelson and Oppen in 1980 (Nelson 1980; Nelson and Oppen 1980), e-graphs received a surge of new attention when Willsey et al demonstrated, via their software package egg, that e-graphs combined with equality saturation can be a fast, powerful, and adaptable tool for equational reasoning (Willsey...| Topos Institute
Introduction What is the world? Is it “everything that is the case?” Does it have different strata, whose realities are grounded in mutually incompatible ways, or just one? When we describe the world to each other, don’t our choices of language privilege certain answers to these questions, and foreclose on the possibility of certain others? I won’t waste much time with monism (i.e. the answer “just one”), even when many fellow Western tech-and-science types seem to take it as not...| Topos Institute
Next week we will be hosting a guest seminar talk in Oxford, co-organised by José Siqueira here at Topos UK, and Sandra Kiefer and Sam Staton at the Oxford University Computer Science department. If you’re around town, then you’re very welcome to attend — you can find a copy of the announcement below. --- Dear all, It is with great pleasure that I announce the start of our TopOx seminar series, a partnership between the Topos Institute and the Oxford University Computer Science departm...| Topos Institute
This is a brief little post about naming. Naming is well-known to be one of the hardest problems in computer science. But why is this the case? I claim that one of the reasons is because often naming systems are being asked to do triple-duty; a single name is used to perform the three functions of reference, identity, and display. What does this mean? Consider a group of people. Each person has a name. However, these names may not be unique. If I want to refer to a person, I might say somethi...| Topos Institute
At last week’s Topos Colloquium, Rory Lucyshyn-Wright told us about categories graded by a monoidal category, following his recent preprint (Lucyshyn-Wright 2025). Graded categories, short for locally graded categories, were first introduced by Richard Wood under a different name (Wood 1976, 1978). Graded categories are of mathematical interest because they simultaneously generalize actions of a monoidal category (“actegories”) and, via a Yoneda-type embedding, enriched categories, whil...| Topos Institute
Communicated by David Spivak. I invited Edmund Harriss to visit Topos Institute last October, because his work on mathematical art so beautifully exemplified the sort of “working language” I’ve been exploring. Mathematical forms (such as a “perfect circle”) can be conceptually overlaid onto a real-world condition (such as an actual piece of paper) and constrain our behavior enough that the form is efficiently materialized (such as by a computer program hooked up to a mill). I found ...| Topos Institute
Communicated by Brendan Fong. I’m delighted to welcome our first philosopher-in-residence, B. Scot Rousse! In getting to know B over the past few months, I’ve been struck by his insights into the ways technologies can centre and marginalise human care and meaning-making, as well as his deep commitment to serving others and building a world that supports this care. We’re very excited to bring B’s rich, distinctive intellectual tradition into Topos. Moreover, I’m excited to explore ho...| Topos Institute
Today’s scientific literature is quickly growing in volume and complexity. The complexity of a modern paper is akin to foreign text without a Rosetta Stone. In turn, our ability to comprehend hasn’t kept pace with our ability to produce. When research is difficult to understand, science slows. But when ideas are communicated clearly, readers can critically engage instead of being stymied by obscurity. Unlike computer programs, academic papers don’t have programmed translators to make se...| Topos Institute
You can find a link to the full interview on Eric’s blog below: A Category Theory-Inspired BBN How the Topos Institute tackles problems in complex systems In putting together this piece, Brendan and I had over three hours of messy, wide-ranging conversations and interviews. We've distilled them into this final, more readable, interview format. Full post| Topos Institute
I’d like to thank David Spivak for his contributions to this post and for his guidance and supervision for this project.1 1 Library reform Libraries collect and organize human knowledge, equipping people with the ability to access, learn, and build upon others’ ideas. In turn, today’s society is equipped to handle problems that are more complex than at any point in history. Still, there is more to document and the scope of our libraries could be meaningfully larger. By expanding what we...| Topos Institute
We’re pushing out a major release comprising our CatColab work over the last quarter. If you’re just tuning in to the project, see my first blog post on the topic. This is an alpha release, that is, CatColab is still experimental software with many features on the roadmap. However, we now have a more full-featured user-accessible database for storing, saving, and sharing your models, and we intend to migrate your data along with all future updates. Therefore, from today, we think CatColab...| Topos Institute
[Ed.] C.B. has provided a much better typeset PDF version of this blog post. Dependent types are ubiquitous in mathematics, pure and applied. When we say “let be a vector of length ,” we make the collection of values to which may belong dependent upon the value of . Such dependency of types-of-things on values-of-things is fundamental to our ability to express complex mathematical ideas and build up sophisticated abstractions. By taking this essential idea to heart, dependent type theory ...| Topos Institute
One of our central goals here at Topos is to enable a variety of different people with different domains of expertise and interest to collaborate on the design and analysis of conceptually defined models. For people to collaborate on the modelling process, we’ll need a version control system for models. A core tenet of our approach to modelling is that models — both the concepts involved and any measured data — should themselves be structured data and not just the code that describes ho...| Topos Institute
Growing the Topos tech team| Topos Institute