![[Berkeley Seminar] Kevin Carlson (Topos Institute) | Exponentiability @ToposInstitute](https://i.ytimg.com/vi/9Kr-Oigw9bg/maxresdefault.jpg)
Uploaded June 2026 | Updated September 2026, 2 weeks ago
Title: Exponentiability
Abstract: I’ll report on Ea Thompson and my recent preprint, discussing how to classify cocontinuous functors on categories of models of a sketch, with immediate applications to exponentiability in general, and how we reduce the general result to manageable conditions in the case of exponentiable virtual double categories.
Date: June 16, 2026
Title: Exponentiability
Abstract: I’ll report on Ea Thompson and my recent preprint, discussing how to classify cocontinuous functors on categories of models of a sketch, with immediate applications to exponentiability in general, and how we reduce the general result to manageable conditions in the case of exponentiable virtual double categories.
Date: June 16, 2026
![[Berkeley Seminar] Kevin Carlson (Topos Institute) | Exponentiability](https://i.ytimg.com/vi/9Kr-Oigw9bg/mqdefault.jpg "[Berkeley Seminar] Kevin Carlson (Topos Institute) | Exponentiability
Title: Exponentiability
Abstract: I’ll report on Ea Thompson and my recent preprint, discussing how to classify cocontinuous functors on categories of models of a sketch, with immediate applications to exponentiability in general, and how we reduce the general result to manageable conditions in the case of exponentiable virtual double categories.
Date: June 16, 2026")
![[DOTS Lectures] 12. A general representability theorem for Systems Theory Pt. 2](https://i.ytimg.com/vi/A4GaF2eAodY/mqdefault.jpg "[DOTS Lectures] 12. A general representability theorem for Systems Theory 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")
![[Berkeley Seminar] Harrison Grodin | Amortized Analysis via Coalgebra](https://i.ytimg.com/vi/A4TTyeVsheM/mqdefault.jpg "[Berkeley Seminar] Harrison Grodin | Amortized Analysis via Coalgebra
Title: Amortized Analysis via Coalgebra
Abstract: Amortized analysis is a technique for analyzing the efficiency of operations on a data structure in which cost is studied in aggregate: rather than considering the cost of a single operation in isolation, one bounds the total cost encountered throughout multiple operations in sequence. Traditionally, amortized analysis is phrased inductively, quantifying over finite sequences of operations. Connecting to prior work on coalgebraic semantics for data structures, we develop the alternative perspective that amortized analysis is naturally viewed coalgebraically in a category of cost algebras. In addition to simplifying the precise definition of amortized analysis, this perspective also generalizes the technique to other settings and incorporates type- and category-theoretic intuition.
https://topos.institute/events/berkeley-seminar/")
![[Oxford Seminar] Matteo Capucci | A Second Taste of Quantitative Logic](https://i.ytimg.com/vi/BAwK-X-8pIw/mqdefault.jpg "[Oxford Seminar] Matteo Capucci | A Second Taste of Quantitative Logic
Oxford Seminar, December 4 2025
Speaker: Matteo Capucci
Full Title: A Second Taste of Quantitative Logic
Abstract: In this second talk I will introduce p-means and argue they form a good quantitative analogue of first-order quantifiers. I will then sketch the construction of a hyperdoctrine valued in enriched graded preorders which forms the intended semantics of a first-order quantitative linear logic.")
![[DOTS Lectures] 13. A general representability theorem for Systems Theory Pt. 3](https://i.ytimg.com/vi/BST8hBWS1Kw/mqdefault.jpg "[DOTS Lectures] 13. A general representability theorem for Systems Theory Pt. 3
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")
![[2-torial] Quantum information theory, Part 3: Quantum bird watching](https://i.ytimg.com/vi/BfX-vy47fZw/mqdefault.jpg "[2-torial] Quantum information theory, Part 3: Quantum bird watching
2-torial, May 20 2026
You can find accompanying notes and other information on this video at https://topos.institute/work/lectures/2-torials/2026-05-20_hosgood_quantum/
Tutor: Tim Hosgood
Tutee: Jason Brown
The elements of quantum information theory are not so complicated: some linear algebra over the complex numbers and a bit of classical probability theory. But it doesnt take long before you run into some intriguing problems that showcase how established experimental results contradict our classical intuition. In this 2-torial we will learn the very basics of quantum theory, see how a Mach–Zehnder interferometer gives a real-world implementation of a classically impossible construction and suggests that we should go all in on complex numbers, and finally how this all applies to the world of theoretical bird watching via the Quantum Zeno effect.")
![[Berkeley Seminar] Ea Thompson | A Characterization of Pro-representable Virtual Double Categories](https://i.ytimg.com/vi/CLwKSyVtjLc/mqdefault.jpg "[Berkeley Seminar] Ea Thompson | A Characterization of Pro-representable Virtual Double Categories
Title: A Characterization of Pro-representable Virtual Double Categories
Abstract: Virtual double categories have been shown to provide an effective framework for formal category theory, from characterizations of adjoints and liftings to descriptions of pointwise Kan extensions and Yoneda structures. In studying virtual double categories themselves, an interesting question comes from asking what kind of structure virtual double categories are enriched over. In this talk, we take a first step in answering this question by characterizing the exponentiable, or pro-representable, virtual double categories. We will provide examples of pro-representable virtual double categories, including pseudo double categories and cospan virtual double categories, while also providing a simple counter-example to the claim that all virtual double categories are exponentiable. If there is time, we will discuss another internal-hom candidate coming from Libkind, Myers, Carlson, and Brown’s theory of loose bimodules.")
