![[Berkeley Seminar] Keri DAngelo | Composing Instantaneous Machines @ToposInstitute](https://i.ytimg.com/vi/FevtvBgF1RU/maxresdefault.jpg)
Uploaded October 2024 | Updated September 2026, 2 weeks ago
Title: Composing Instantaneous Machines
Abstract: In this talk, I’ll discuss recent progress Sophie and I have made on composing instantaneous machines. Instantaneous machines means that at any point in time, input can be given to the machine and the machine will give output based on this input and its current state. In this talk, I’ll show how we can compose such machines. We first create an extended category of directed wiring diagrams accounting for the dependency between input and output, and then define an operad algebra giving us the semantics that defines composition. Depending on where the interest lies, we can delve into some details including that since the output now depends on the input, we come into the “problem” that every time the output changes, the input may also change. This can be accounted for by giving a fixed point that shows after finite time, our input and output will stabilize.
https://topos.site/events/berkeley-seminar/
Title: Composing Instantaneous Machines
Abstract: In this talk, I’ll discuss recent progress Sophie and I have made on composing instantaneous machines. Instantaneous machines means that at any point in time, input can be given to the machine and the machine will give output based on this input and its current state. In this talk, I’ll show how we can compose such machines. We first create an extended category of directed wiring diagrams accounting for the dependency between input and output, and then define an operad algebra giving us the semantics that defines composition. Depending on where the interest lies, we can delve into some details including that since the output now depends on the input, we come into the “problem” that every time the output changes, the input may also change. This can be accounted for by giving a fixed point that shows after finite time, our input and output will stabilize.
https://topos.site/events/berkeley-seminar/
![[Berkeley Seminar] Keri DAngelo | Composing Instantaneous Machines](https://i.ytimg.com/vi/FevtvBgF1RU/mqdefault.jpg "[Berkeley Seminar] Keri DAngelo | Composing Instantaneous Machines
Title: Composing Instantaneous Machines
Abstract: In this talk, I’ll discuss recent progress Sophie and I have made on composing instantaneous machines. Instantaneous machines means that at any point in time, input can be given to the machine and the machine will give output based on this input and its current state. In this talk, I’ll show how we can compose such machines. We first create an extended category of directed wiring diagrams accounting for the dependency between input and output, and then define an operad algebra giving us the semantics that defines composition. Depending on where the interest lies, we can delve into some details including that since the output now depends on the input, we come into the “problem” that every time the output changes, the input may also change. This can be accounted for by giving a fixed point that shows after finite time, our input and output will stabilize.
https://topos.site/events/berkeley-seminar/")
![[2-torial] Kevin tells Jason and David about instances of models of double theories](https://i.ytimg.com/vi/GJMBFPe7T6I/mqdefault.jpg "[2-torial] Kevin tells Jason and David about instances of models of double theories
21st of November 2025
Kevin Carlson has recently written a paper, Instances of models of double-categorical theories (https://arxiv.org/abs/2510.08861), with Evan Patterson. Here he explains to David and Jason what instances are and why theyre interesting.")
![[DOTS Lectures] 7. Symmetric monoidal double categories of systems](https://i.ytimg.com/vi/GrGJ58O1NKg/mqdefault.jpg "[DOTS Lectures] 7. Symmetric monoidal double categories of systems
Part of a lecture series on the Double Operadic Theory of Systems (DOTS) presented by David Jaz Myers.")
![[Oxford Seminar] Joanna Ko | Models of Enhanced 2-sketches & Algebras over Enhanced 2-monads](https://i.ytimg.com/vi/HDrcpYeSJhU/mqdefault.jpg "[Oxford Seminar] Joanna Ko | Models of Enhanced 2-sketches & Algebras over Enhanced 2-monads
Oxford Seminar, June 18 2026
You can view the listing for this talk online at https://topos.institute/events/oxford-seminar/talks/2026-06-18_ko_models.html
Speaker: Joanna Ko
Full Title: Models of Enhanced 2-sketches & Algebras over Enhanced 2-monads
Abstract: We study the enhanced 2-category of models of enhanced limit 2-sketches with tight weighted cones. We show that for any enhanced limit 2-sketch (mathbb{T}) with tight cones, the enhanced 2-category (mathbb{M}mathrm{od}_{s, w}(mathbb{T}, mathbb{K})) of models of (mathbb{T}) in a locally presentable enhanced 2-category (mathbb{K}), in which the tight and the loose morphisms are the (mathscr{F})-natural transformations and the loose (w)-natural transformations, respectively, is equivalent to the enhanced 2-category ({mathrm{T}text{-}mathbb{A}mathrm{lg}}_{s, w}) of algebras over an enhanced 2-monad (T) on the models (mathbb{M}mathrm{od}(mathcal{T}_tau, mathbb{K})) restricted to the tight morphisms in (mathbb{T}) with strict (T)-morphisms and (w)-(T)-morphisms.
Along the way, we establish an enriched analogue of the Orthogonal Sub-category Theorem, and generalise results on the reflectivity and the monadicity of models of enriched limit sketches in the base of enrichment to any arbitrary locally presentable enriched category.")
![[Berkeley Seminar] Kevin Carlson | What is it like to be a lax double functor?](https://i.ytimg.com/vi/IFQgqey_388/mqdefault.jpg "[Berkeley Seminar] Kevin Carlson | What is it like to be a lax double functor?
Title: What is it like to be a lax double functor?
Abstract: I will attempt to impart the vibe that the models of double theories that are the basis of CatColab are certain kinds of families of categories, even though the definition looks like a generalization of the families of sets we know and love as presheaves. Furthermore, CatColab does (on a sufficiently bleeding-edge branch) contain families of sets that live over these families of categories in an appropriate way, which we call instances of models of double theories. (Deep breath.) Probably only two people know what those are, yet, so let me try to tell you, because theyre going to be important; its not all that bad, just new.
https://topos.site/events/berkeley-seminar/")
![[DOTS Lectures] 19. State Sharing Pt. 2](https://i.ytimg.com/vi/IR0Y52DNYyo/mqdefault.jpg "[DOTS Lectures] 19. State Sharing Pt. 2
Part of a lecture series on the Double Operadic Theory of Systems (DOTS) presented by David Jaz Myers.
Some material from these lectures can be found in Davids book on categorical systems theory:
https://www.davidjaz.com/Papers/DynamicalBook.pdf")
![[Oxford Seminar] Owen Lynch | Element Model Type Theory](https://i.ytimg.com/vi/Id-9XE5TsA8/mqdefault.jpg "[Oxford Seminar] Owen Lynch | Element Model Type Theory
Oxford Seminar, 6th of March 2025
Generalized algebraic theories have long been part of our work at Topos, going back to the very beginnings of Catlab.jl. In this talk, I give a new implementation of generalized algebraic theories in Rust, which takes a different, more type-theoretic approach to generalized algebraic theories. This approach tightly integrates e-graphs into the type-checking process to enable an approximation to extensive equality, and in addition enables greater compositionality of theories, achieving a principled approach to “theory pushout” that has been long-desired. This new implementation is intended as a prototype for type-checking algorithms that will go into CatColab and enable “open notebooks” for compositional modeling, and I give an overview of how I envision that working. In addition to this application in scientific modeling, I believe that lessons from this implementation that I have learned about two-level type theory could be applicable in a wide variety of domains in which abstraction is desired that does not complicate the underlying semantics, such as finite state machines, probabilistic programming, SAT solving, systems programming, constraint programming, databases, and serialization formats.")
![[Oxford Seminar] Tim Hosgood | Why might I want to build a formal model for a respiratory virus?](https://i.ytimg.com/vi/Iva9fmr-uic/mqdefault.jpg "[Oxford Seminar] Tim Hosgood | Why might I want to build a formal model for a respiratory virus?
Oxford Seminar, March 12 2026
Speaker: Tim Hosgood
Full Title: Why might I want to build a formal model for a respiratory virus?
Abstract: At the risk of giving a talk completely lacking structure, Id like to jump around a bit and try to answer a few different questions:
1. How can formal modelling software, like CatColab, help people to better understand scientific models outside their expertise?
2. What do we mean when we say things like categorical modelling can help make assumptions explicit?
3. How can we allow for somewhat informal-looking diagrams to convey precise quantitative information?
4. What does it look like, in practice, to add new functionality to CatColab?
In reality, of course, I spent weeks before I realised that these were actually the questions that I was interested in, let alone before I was able to come up with some answers. Here, Ill try to disentangle things a bit and present a cleaner story.
This talk will be split into two parts: the first 45 minutes will be for a general audience, followed by a 20 minute technical discussion with a brief coffee break in between.")
