Uploaded December 2025 | Updated September 2026, 2 weeks ago
Topos Institute Colloquium, 11th of December 2025.
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Cospans of finite sets are the morphisms in a bicategory, not really a category, because composition of cospans is associative only up to natural isomorphism. How can we characterize this bicategory abstractly? There's a category of finite sets and *isomorphism classes* of cospans. Steve Lack gave a beautiful characterization of this, which I will explain, and Fong and Spivak used this category to clarify the concept of "hypergraph category". But what about the *bicategory* of finite sets, cospans, and maps between cospans? I will state a guess that I haven't proved.
Topos Institute Colloquium, 11th of December 2025.
———
Cospans of finite sets are the morphisms in a bicategory, not really a category, because composition of cospans is associative only up to natural isomorphism. How can we characterize this bicategory abstractly? There's a category of finite sets and *isomorphism classes* of cospans. Steve Lack gave a beautiful characterization of this, which I will explain, and Fong and Spivak used this category to clarify the concept of "hypergraph category". But what about the *bicategory* of finite sets, cospans, and maps between cospans? I will state a guess that I haven't proved.
![[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.")
![[Oxford Seminar] Matteo Capucci | A Taste of Quantitative Logic](https://i.ytimg.com/vi/JWfuuPr_ptU/mqdefault.jpg "[Oxford Seminar] Matteo Capucci | A Taste of Quantitative Logic
Oxford Seminar, November 26 2025
Speaker: Matteo Capucci
Full Title: A Taste of Quantitative Logic
Abstract: Quantitative logic, after Lawvere, is one whose judgments are valued in real numbers, rather than merely being a logic about real numbers. By doing this we can guarantee good structural properties of the logic, such as being able to treat addition as an additive connective in the sense of Girard. Moreover, by employing the full spectrum of sums multiplication distributes over, we are able to approximate hard connectives with soft ones, with application in machine learning. In the talk I will showcase these features by describing a sequent calculus for a quantitative version of linear logic. This is work in progress with Atkey, Grellois, and Komendantskaya.")
![[Berkeley Seminar] Kris Brown | Incremental homomorphism search](https://i.ytimg.com/vi/LUOOSz1f-80/mqdefault.jpg "[Berkeley Seminar] Kris Brown | Incremental homomorphism search
Title: Incremental homomorphism search
Abstract: An incremental search problem tries to answer how the answer set to some query changes in response to a relatively small change to underlying ground truth data. This can be much more efficient than trying to compute the answer to the new data from scratch. Moreover, in many contexts we have a fixed set of possible changes that we are anticipating, so our algorithm ought to take advantage of this extra knowledge. Well first address this in the context of relational databases, which we model as ACSets, with the set of ACSet homomorphisms Hom(Q, X) being the answer set to a query Q, which is itself an ACSet. Then well generalize this story to any category with appropriate structure. This is work-in-progress, which you can check out at https://www.krisb.org/forest/math-00IG.xml.
https://topos.institute/events/berkeley-seminar/")
![[Oxford Seminar] Ray Pedersen | Everettian QM and the problem of ontological extravagance](https://i.ytimg.com/vi/L_PKQhLrWRs/mqdefault.jpg "[Oxford Seminar] Ray Pedersen | Everettian QM and the problem of ontological extravagance
Oxford Seminar, 27th of March 2025
Title: Everettian quantum mechanics and the problem of ontological extravagance
Abstract: Since it neither relies on a collapse postulate nor posits a hidden variable, Everettian quantum mechanics (EQM) is an attractive option among realist interpretations of quantum mechanics. In some sense, EQM is a simpler theory than its competitors. However, it also appears to require more structure; unlike its competitor theories, EQM has traditionally been taken to entail a multitude of worlds, as every possible outcome of every quantum process is actualized in at least one world. Since no other realist competitor theory shares this feature, the most prominent objection raised against EQM is that of ontological extravagance.
Everettians have given this objection little serious attention, at least in part because the objection from ontological extravagance has not yet been carefully articulated in the literature. To clarify this objection, I distinguish between two types of simplicity criteria: ones concerned with ontological abundance and others concerned with postulate abundance. Where ontological abundance criteria concern the number of concrete objects that some theory posits, postulate abundance norms instead concern the number and overall complexity of the set of postulates of the theory. Unfortunately, it is unclear how we ought to weigh these simplicity-related metaphysical considerations, and worse, as I argue, there is no independent motivation for either sort. I argue that we ought to instead consider the proximity between the way the theory says the world is, and the way the world appears to be. With the deadlock between Everettians and non-Everettians on what sort of simplicity criterion reigns supreme, this severely overlooked criterion offers a promising route forward in the dialectic. This alternate criterion roughly corresponds to what Emery (2023) calls the minimal divergence norm, under which we ought to prefer theories that deviate least from the manifest image, or the way the world generally appears to be. However, such a norm requires further specification; there is no image of the world that uniquely picks out the manifest image. Observations themselves depend on our theoretical commitments, which vary from agent to agent, and so there are many manifest images. To avoid this multiplicity, I argue that we ought to look to the physical sciences for a widely-accepted theory that describes the world as we experience it. Classical mechanics (CM), the predecessor theory to quantum mechanics, does exactly that; though it is certainly not a correct description of reality, it is sufficiently accurate for numerous forms of engineering, as it describes macroscopic reality well enough. I argue that we ought to treat the way that classical mechanics says the world is as the manifest image. Then, the third type of criteria, which I call classical divergence, concerns the degree to which the way some theory in question says the world is deviates from the way that CM says the world is. I defend this norm on pragmatic grounds, arguing that adhering to it offers a distinct epistemic advantage.
While EQM does not necessarily tell us that our world is vastly different from the way that CM says it is, it is generally taken to entail many more worlds than its competitor theories. With this new set of simplicity criteria in place, Everettians can better understand the available dimensions along which they may endeavor to improve their ontology. This new norm that I advocate offers hope: Everettians can seek a less extravagant ontology by strategically minimizing classical divergence.")
