Uploaded March 2026 | Updated September 2026, 2 weeks ago
Topos Institute Colloquium, 5th of March 2026
———
We will go over the basics of duoidal categories, illustrating with a number of examples. As monoidal categories provide a context for monoids, duoidal categories provide one for duoids and bimonoids. Our main goal is to discuss a number of versions of the classical Eckmann-Hilton argument which may be formulated in this setting. As an application we will obtain the commutativity of the cup product on the cohomology of a bimonoid with coefficients in a duoid, an extension of a familiar result for group and bialgebra cohomology with trivial coefficients.
The talk borrows on earlier work in collaboration with Swapneel Mahajan on the foundations of duoidal categories (2010). The main results are from ongoing work with Javier Coppola. We also rely on work of Richard Garner and Ignacio López-Franco (2016).
Topos Institute Colloquium, 5th of March 2026
———
We will go over the basics of duoidal categories, illustrating with a number of examples. As monoidal categories provide a context for monoids, duoidal categories provide one for duoids and bimonoids. Our main goal is to discuss a number of versions of the classical Eckmann-Hilton argument which may be formulated in this setting. As an application we will obtain the commutativity of the cup product on the cohomology of a bimonoid with coefficients in a duoid, an extension of a familiar result for group and bialgebra cohomology with trivial coefficients.
The talk borrows on earlier work in collaboration with Swapneel Mahajan on the foundations of duoidal categories (2010). The main results are from ongoing work with Javier Coppola. We also rely on work of Richard Garner and Ignacio López-Franco (2016).
![[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.")
