Uploaded October 2025 | Updated September 2026, 2 weeks ago
Topos Institute Colloquium, 9th of October 2025.
———
Behavioural distances of transition systems modelled via coalgebras for
endofunctors generalize traditional notions of behavioural equivalence
to a quantitative setting, in which states are equipped with a measure
of how (dis)similar they are. Endowing transition systems with such
distances essentially relies on the ability to lift functors describing
the one-step behavior of the transition systems to the category of
pseudometric spaces. We consider the category theoretic generalization
of the Kantorovich/Wasserstein lifting from transportation theory to the
case of lifting functors to pseudo-metric spaces. We also consider
compositionality results which are essential ingredients for adapting
up-to-techniques to the case of behavioural distances. Up-to techniques
are a well-known coinductive technique for efficiently showing lower
bounds for behavioural metrics. We illustrate the method with a case
study on probabilistic automata.
This is joint work with Paolo Baldan, Filippo Bonchi, Henning Kerstan,
Daniela Petrisan, Keri D'Angelo, Sebastian Gurke, Johanna Maria Kirss,
Matina Najafi, Wojciech Rozowski and Paul Wild.
Topos Institute Colloquium, 9th of October 2025.
———
Behavioural distances of transition systems modelled via coalgebras for
endofunctors generalize traditional notions of behavioural equivalence
to a quantitative setting, in which states are equipped with a measure
of how (dis)similar they are. Endowing transition systems with such
distances essentially relies on the ability to lift functors describing
the one-step behavior of the transition systems to the category of
pseudometric spaces. We consider the category theoretic generalization
of the Kantorovich/Wasserstein lifting from transportation theory to the
case of lifting functors to pseudo-metric spaces. We also consider
compositionality results which are essential ingredients for adapting
up-to-techniques to the case of behavioural distances. Up-to techniques
are a well-known coinductive technique for efficiently showing lower
bounds for behavioural metrics. We illustrate the method with a case
study on probabilistic automata.
This is joint work with Paolo Baldan, Filippo Bonchi, Henning Kerstan,
Daniela Petrisan, Keri D'Angelo, Sebastian Gurke, Johanna Maria Kirss,
Matina Najafi, Wojciech Rozowski and Paul Wild.
![[Berkeley Seminar] Brendan Fong | Processes of Production of Abstraction](https://i.ytimg.com/vi/WzAPGmW5YHQ/mqdefault.jpg "[Berkeley Seminar] Brendan Fong | Processes of Production of Abstraction
Title: Category Theory as the Formal Study of the Processes of Production of Abstraction
Abstract: For the last few months I’ve been reflecting on the phrase “Category theory is the formal study of the processes of production of abstraction”. I’ll say some words about what this phrase means to me. I ask your help inquiring about the epistemology of these meditations.
Date: 2025-06-10
https://topos.institute/events/berkeley-seminar/")
![[Oxford Seminar] David Jaz Myers | Compositionality via 2-algebra](https://i.ytimg.com/vi/XXIaJ98SUik/mqdefault.jpg "[Oxford Seminar] David Jaz Myers | Compositionality via 2-algebra
Oxford Seminar, May 28 2026
Speaker: David Jaz Myers
Full Title: Compositionality via 2-algebra
Abstract: A complex system may be designed modularly by putting together interacting component subsystems. Since analyses of complex systems can often scale very poorly with their size, it pays to use the modular structure of such systems to divide the task of analysis across the component subsystems.
Many analyses of systems may be encoded as homomorphism search problems between systems of the same sort. This suggests attending to categories of systems and their homomorphisms. In this talk, well consider the modular structure of a class of systems as a 2-algebra — an algebraic structure on categories of systems (and their interfaces and interaction patterns). Well see compositionality theorems as (lax) homomorphisms of these 2-algebraic structures, and survey a number of techniques for proving them using 2-categorical algebra.")
![[DOTS Lectures] 8. Compositionality of behaviours: generalized Moore machine case](https://i.ytimg.com/vi/Xxo8Om-pBn8/mqdefault.jpg "[DOTS Lectures] 8. Compositionality of behaviours: generalized Moore machine case
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] Tim Hosgood | Homotopy coherent Bousfield–Kan](https://i.ytimg.com/vi/Y9w6YzhEaoo/mqdefault.jpg "[Oxford Seminar] Tim Hosgood | Homotopy coherent Bousfield–Kan
Oxford Seminar, July 30 2026
You can view the listing for this talk online at https://topos.institute/events/oxford-seminar/talks/2026-07-30_hosgood_bousfield.html
Speaker: Tim Hosgood
Full Title: Homotopy coherent Bousfield–Kan
Abstract: From a weird little-known construction in complex geometry we can notice a new type of subdivision of simplices: half cubical, half simplicial, and very useful for working with certain geometric objects. These subdivisions are called /homotopy-coherent simplices/ (previously /wiggly simplices/).
In this talk I will give an introduction to the theory and methodology of homotopy limits of cosimplicial spaces through some tools of 2-category theory, explaining the important construction of Bousfield–Kan, and how this generalises to the homotopy coherent setting following joint work with Jason Brown and Cheyne Glass. I will also show lots of pictures of triangles. If times permits, I will introduce the notion of /homotopy homotopy limit/.
/Prerequisites./ The talk will use Quillen model categories and cosimplicial simplicial sets, but I will try to give good enough speedy overviews of both of these definitions. I will also use some definitions from enriched category theory (namely weighted (co)limits) but in a way that will likely make any Australians in the room rather upset.
/Recommended pre-reading./ The following definitions: nerve of a category, barycentric subdivision of a simplex, simplicial set.")
