Uploaded July 2026 | Updated September 2026, 2 weeks ago
Topos Institute Colloquium, 16th of July 2026.
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In higher category theory, there is a long tradition of describing certain restricted classes of polygraphs as explicitly as possible (cf. Johnson, Street, Steiner, Forest, Hadzihasanovic,...). A sufficiently explicit description deserves to be called a "pasting theorem" after Power. Classically, this work takes place in the setting of strict n-categories and strict polygraphs.
In this talk, I will discuss similar theorems for weak $(\infty,n)$-categories. For sufficiently restricted classes of polygraphs $P$ (e.g. $P$ could be a loop-free Steiner complex), the $(\infty,n)$-categorical pasting theorem says that the free weak $(\infty,n)$-category generated by $P$ coincides with the free strict $n$-category generated by $P$, so that prior strict results can be imported directly. This extends previous results of Columbus, and of Hackney-Ozornova-Riehl-Rovelli in dimension 2.
I will also discuss a recent generalization due to Chanavat which goes beyond the loop-free case.
Topos Institute Colloquium, 16th of July 2026.
———
In higher category theory, there is a long tradition of describing certain restricted classes of polygraphs as explicitly as possible (cf. Johnson, Street, Steiner, Forest, Hadzihasanovic,...). A sufficiently explicit description deserves to be called a "pasting theorem" after Power. Classically, this work takes place in the setting of strict n-categories and strict polygraphs.
In this talk, I will discuss similar theorems for weak $(\infty,n)$-categories. For sufficiently restricted classes of polygraphs $P$ (e.g. $P$ could be a loop-free Steiner complex), the $(\infty,n)$-categorical pasting theorem says that the free weak $(\infty,n)$-category generated by $P$ coincides with the free strict $n$-category generated by $P$, so that prior strict results can be imported directly. This extends previous results of Columbus, and of Hackney-Ozornova-Riehl-Rovelli in dimension 2.
I will also discuss a recent generalization due to Chanavat which goes beyond the loop-free case.
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Oxford Seminar, 21st of August 2025
Title: There is No Band: Double Categories, Fragmented Spacetime, and an AQFT
Abstract: David Lynchs neo-noir classic Mulholland Drive challenges our sense of continuity, identity, and causality. In this talk, I use its fragmented narrative structure as a metaphorical guide to construct an algebraic quantum field theory using a double functor between free globularly generated double categories.
We define a double category of spacetime regions where vertical morphisms are inclusions, horizontal morphisms are causal maps, and squares ensure compatibility between the two. On the algebra side, we use Juan Orendains double category of von Neumann algebras and bimodules using a general construction from decorated bicategories. The result is a functor that captures how observables evolve and embed across spacetime in a way that traditional approaches don’t cleanly separate. We discuss how gluing and locality can be modelled in this construction.
Along the way, we use the storyline of Mulholland Drive to guide our intuition and structure the talk — from fragments of time and overlapping realities to a new way of understanding gluing and locality in field theory. No background in physics is assumed — just curiosity, and a willingness to follow a story where not everything is what it seems.")
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Part of a lecture series on the Double Operadic Theory of Systems (DOTS) presented by David Jaz Myers.")
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Title: Communicating Relational Thinking
Abstract: In this talk I will give an overview of our recently completed experiment of communicating categorical thinking to a STEM-oriented audience outside mathematics. Angeline, Brendan, Paul and myself recently authored a free online textbook titled Relational thinking: from Abstractions to Applications. In this talk, I will walk through the contents of the book and equally importantly the open source technologies behind the book. This talk is an invitation to the audience not only to read the book but also to create their own inclusive material around category theory / math leveraging new technologies.
https://topos.site/events/berkeley-seminar/")
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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")
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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")
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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/")
