Research articles, statements of vision, and more
How we can think about pushouts as applying rules via substitution, featuring examples in categorical databases and Datalog.
Next week we’re co-hosting an in-person seminar talk in Oxford. This post contains the mailing announcement.
Brendan recently spoke with Eric Gilliam and the interview resulted in a blog post on Eric’s blog.
Come spend the summer at the Topos Institute! For early-career researchers, we’re excited to open up applications for our 2025 Summer Research Associate program.
One of the things I do at Topos is make sense of some aspect of the world by articulating it in mathematics. Follow along as I make sense of Bayesian update using the mathematics of polynomial functors.
In the third post of this series about Relational Thinking: from abstractions to applications, we look at the story-telling approach that we took in writing the book.
In the second post of this series about Relational Thinking: from abstractions to applications, we look at the technologies used to build the book.
In the first post of this series, we introduce the freely available online book Relational Thinking: from abstractions to applications, starting with the story of how it came into being and giving a brief overview of its contents.
An interesting analogy between algebras over a ring and promonads on a category is formalized using the apparatus of double theories.
Physical systems are often composed of many interacting subsystems. In this post, we take a peek at the math and the software implementation for composing systems of springs using decorated cospans.
The beginning of a series of posts answering the question “why double categories?”. Our first answer is that double categories give the algebra of relations from universal properties.
An exposition of a philosophical argument about how words connect with their meanings, and a tentative connection to work done at Topos.
This summer I created the StatisticalTheories.jl package so we can do categorical probability and synthesize probabilistic programs in the AlgebraicJulia ecosystem. Read all about it!
John Baez is now helping lead a new Fields Institute program on the mathematics of climate change.
Announcing the first version of InterTypes: a package for cross-language serialization for ADTs and ACSets
Retrotransformations between lax double functors are introduced as the “multi-object” analogue of a cofunctor between categories. Notions of “monoidal cofunctor” between monoidal categories and of “multicofunctor” between multicategories are then derived as special cases.
Cartesian double theories are a new framework for doctrines based on double-categorical functorial semantics.
Many of our favorite monads on \mathbf{Set}, such as the Maybe monad and the List monad, are polynomial. It turns out that monads have special “powers” in \mathbf{Poly}.
Categorifying the observation that monoids are generalized elements of multicategories, we show that unbiased pseudomonoids, such as unbiased monoidal categories, are “pseudo-elements” of 2-multicategories.
Rewrite rules are organized via a graphical syntax into discrete-time simulations which can be understood as agent-based models. This representation is transparent, compositional, and serializable.
We’re delighted to announce that Shaowei Lin has joined Topos as our new Director of Research.
Acsets are great, but what if attributes could be variables?
In this post, we lay out a vision and challenge for using category theory to build tools for understanding systems at a global scope.
A follow-up to Algebraic Geometry for the Working Programmer, this post explains a category-theoretic approach to symbolic open dynamical systems.
Having first heard about theorems on fixed points as an undergraduate, uses for them came into my research on many subsequent occasions. The talk will review some personal history and give some suggestions for possible further applications.
In this series of posts, we investigate the duality between algebra and geometry in order to develop new types of lenses. In this first post, we review some basic ideas about algebraic geometry that will be needed in the coming posts.
The Topos Institute recently hosted “Finding the Right Abstractions for Healthy Systems”, with 24 researchers, mainly from the applied category theory and AI safety communities. This is a post trying to understand what made it successful and some ideas for similar events.
We invite applications to join Topos Institute as a Research Associate (summer 2023) or as a Research Software Engineer (regular position).
YouTube is our most powerful outreach tool. Yet how does it shape who we reach out to? And is this in line with the values of our community?
“Cells that fire together, wire together.” This slogan for Hebbian learning evokes a strategy for reorganization in which an individual strengthens their connection with another if they have similar behavior. Here we give a mathematical account of Hebbian learning as a dynamic monoidal category.
In August, Nate Soares visited the Topos Institute. We told him a little about Poly and Proly, and he told us about what he wanted from a type theory. Probably the high point in the discussion for me is when he drew the following picture of what he wanted from a type theory.
We’re exploring a new role at Topos: Director of Research. We’d love to hear from or about anyone who might be interested!
This post presents a video presentation, originally shown to the Topos Board of Directors, about David’s research program over the past 15 years, from 2007 to present.
What makes a good mathematical model? For recent work at Topos, it’s when the model helps people cooperate to achieve collective goals. This has a few implications for how we design modelling software.
Building on the double Grothendieck construction introduced last time, we explain how decorated cospans are instance of the Grothendieck construction. This perspective suggests a natural generalization of decorated cospans, which we illustrate through several examples.
Over the past six months, we’ve conducted interviews across the Topos community, and drafted and re-drafted our 2021–2024 strategic plan, so that we can coordinate effectively around a shared strategy as well as a shared vision. We’d like to share that plan with you all today.
Come spend the summer at the Topos Institute! For early-career researchers, we’re excited to open up applications for our summer research associate program.
We invite applications to join the Topos Institute as a Research Software Engineer, to work on software for compositional data integration and scientific modeling in the Julia programming language.
This month sees a new person joining the team here at Topos: we’re thrilled to welcome Brandon Shapiro! He’s working with David Spivak on the theory and applications of polynomial functors. We asked him to write a short blog post introducing both himself and his mathematics.
As this calendar year draws to a close, I asked the members of Topos to each write a little bit about what they’ve worked on this year, how things have gone, and what plans they might have for the future. Here’s what they wrote!
Topos is hiring! We invite applicants for a one-year postdoc position, from November 2021, to work on a project related to dynamical systems and data using the language of polynomial functors.
Often in applied category theory, we hear about how systems form categories — categories of systems. But what about when the systems are categories? In this lecture, we introduce the idea of enriched categories, taking the point of view that an enriched category is a sort of dynamical system.
The Em-Cats seminar series that was announced a while back is almost about to start! We will be welcoming our first speaker (Jade Master) on Wednesday the 25th of August. Here is some more information about this opening talk.
Although this blog has only just launched, the Topos Institute has been running quite a few public-facing events over the past five months or so, including a workshop and regular seminar series. With even more on the horizon, let’s take a look at what has been, and will be, going on.
Welcome to the Topos blog! Here you’ll find news and announcements, statements of our visions and projects at Topos, expository articles on topics of interest to the Topos community, and reports of research in progress.
![The map of mathematics [Source]](2023-01-05-preparing-for-networked-mathematics/map.jpg)
![The cohort of Em-Cats speakers and their talk titles/topics. [PDF]](2021-08-24-em-cats-announcement/em-cats-poster.png)
