![[Berkeley Seminar] David Jaz Myers | Categorical Algebra with Segal Conditions @ToposInstitute](https://i.ytimg.com/vi/52AsVTxHXU0/sddefault.jpg)
Uploaded February 2025 | Updated September 2026, 2 weeks ago
Title: Categorical Algebra with Segal Conditions
Abstract: There are many ways to present algebraic structures categorically: monads, Lawvere theories, limit sketches, and more. In this talk, we'll learn about Yet Another Way to Present Algebra (YAWPA): Segal conditions and Chu and Haugseng's algebraic patterns. The basic idea behind algebraic patterns is that in many cases of categorical algebra we have a notion of *pasting diagram* which tells us how we are going to compose things. These pasting diagrams are made out of elementary features --- things like boxes and wires --- and can "swallow other diagrams whole" by putting subdiagrams into boxes. These two kinds of morphisms, diagram inclusions and "swallowings", organize into a factorization system on a category of pasting diagrams. Presheaves on this category of diagrams which send any pasting diagram to the limit over all its elementary subdiagrams is an algebra composing according to those pasting diagrams; that single axiom is the so-called "Segal condition". We'll see how this works for categories and double categories in particular, and, time-permitting, see how to derive the notion of "virtual double category" from the algebraic pattern for categories and muse about the appropriate "virtual triple categories" which are similarly derived from the algebraic pattern for double categories.
https://topos.institute/events/berkeley-seminar/
Title: Categorical Algebra with Segal Conditions
Abstract: There are many ways to present algebraic structures categorically: monads, Lawvere theories, limit sketches, and more. In this talk, we'll learn about Yet Another Way to Present Algebra (YAWPA): Segal conditions and Chu and Haugseng's algebraic patterns. The basic idea behind algebraic patterns is that in many cases of categorical algebra we have a notion of *pasting diagram* which tells us how we are going to compose things. These pasting diagrams are made out of elementary features --- things like boxes and wires --- and can "swallow other diagrams whole" by putting subdiagrams into boxes. These two kinds of morphisms, diagram inclusions and "swallowings", organize into a factorization system on a category of pasting diagrams. Presheaves on this category of diagrams which send any pasting diagram to the limit over all its elementary subdiagrams is an algebra composing according to those pasting diagrams; that single axiom is the so-called "Segal condition". We'll see how this works for categories and double categories in particular, and, time-permitting, see how to derive the notion of "virtual double category" from the algebraic pattern for categories and muse about the appropriate "virtual triple categories" which are similarly derived from the algebraic pattern for double categories.
https://topos.institute/events/berkeley-seminar/
![[Berkeley Seminar] David Jaz Myers | Categorical Algebra with Segal Conditions](https://i.ytimg.com/vi/52AsVTxHXU0/mqdefault.jpg "[Berkeley Seminar] David Jaz Myers | Categorical Algebra with Segal Conditions
Title: Categorical Algebra with Segal Conditions
Abstract: There are many ways to present algebraic structures categorically: monads, Lawvere theories, limit sketches, and more. In this talk, well learn about Yet Another Way to Present Algebra (YAWPA): Segal conditions and Chu and Haugsengs algebraic patterns. The basic idea behind algebraic patterns is that in many cases of categorical algebra we have a notion of *pasting diagram* which tells us how we are going to compose things. These pasting diagrams are made out of elementary features things like boxes and wires and can swallow other diagrams whole by putting subdiagrams into boxes. These two kinds of morphisms, diagram inclusions and swallowings, organize into a factorization system on a category of pasting diagrams. Presheaves on this category of diagrams which send any pasting diagram to the limit over all its elementary subdiagrams is an algebra composing according to those pasting diagrams; that single axiom is the so-called Segal condition. Well see how this works for categories and double categories in particular, and, time-permitting, see how to derive the notion of virtual double category from the algebraic pattern for categories and muse about the appropriate virtual triple categories which are similarly derived from the algebraic pattern for double categories.
https://topos.institute/events/berkeley-seminar/")
![[Oxford Seminar] Olga Paris-Romanskevich | Gender and science: what every mathematician should know](https://i.ytimg.com/vi/5Zmlp2bmhmI/mqdefault.jpg "[Oxford Seminar] Olga Paris-Romanskevich | Gender and science: what every mathematician should know
Oxford Seminar, April 30 2026
Speaker: Olga Paris-Romanskevich
Full Title: Which results on gender and science every mathematician should
know
Abstract: Based on a selection of works in social psychology, sociology and cultural studies, I will discuss several epistemological approaches of how one can think the exclusion of women and gender minorities from sciences and mathematics in particular. In the discussion following the talk, we will collectively approach what can be done, at the individual and collective level, in order to prevent violence and exclusion from happening.")
![[Oxford Seminar] Owen Lynch | Markov Semigroups](https://i.ytimg.com/vi/5bBPz4GpBIw/mqdefault.jpg "[Oxford Seminar] Owen Lynch | Markov Semigroups
Oxford Seminar, 14th of February 2025")
![[DOTS Lectures] 15. Representability of reachability and double operad algebras](https://i.ytimg.com/vi/6UGVkOVvM5U/mqdefault.jpg "[DOTS Lectures] 15. Representability of reachability and double operad algebras
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] Jason tells Tim about Doctrinal Adjunctions](https://i.ytimg.com/vi/6oDQcA6dU8w/mqdefault.jpg "[2-torial] Jason tells Tim about Doctrinal Adjunctions
[2-torial] Jason tells Tim about Doctrinal Adjunctions")
![[Berkeley Seminar] B. Rousse | Heidegger, Skill, and the Conversational Structure of Human Work](https://i.ytimg.com/vi/6xwODsGadn4/mqdefault.jpg "[Berkeley Seminar] B. Rousse | Heidegger, Skill, and the Conversational Structure of Human Work
Title: Heidegger, Skill, and the Conversational Structure of Human Work
Abstract: AI is transforming how we think about work and intelligence. Many are claiming that AI systems will soon be able to do all the work that human beings do. This claim has a long and somewhat dubious history in the field of AI. To assess its plausibility, it helps to develop a deeper account of the nature of human work and agency. In this talk, I share work in progress aimed at this goal. I trace a tradition that runs from Heidegger’s ontology of human agency, to the theory of skilled activity articulated by Stuart and Hubert Dreyfus (the Dreyfus Skill Model), to the account of the conversational structure of human work developed by Terry Winograd and Fernando Flores in Understanding Computers and Cognition.
Date: 2025-04-29
https://topos.institute/events/berkeley-seminar/")
![[Oxford Seminar] Khyathi Komalan | There is No Band (AQFT and Double Categories)](https://i.ytimg.com/vi/7kMZ8P0hNJo/mqdefault.jpg "[Oxford Seminar] Khyathi Komalan | There is No Band (AQFT and Double Categories)
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.")
![[DOTS Lectures] 5. Composing more Moore Machines](https://i.ytimg.com/vi/88TFFrngyYI/mqdefault.jpg "[DOTS Lectures] 5. Composing more Moore Machines
Part of a lecture series on the Double Operadic Theory of Systems (DOTS) presented by David Jaz Myers.")
![[Berkeley Seminar] Priyaa Srinivasan: Communicating Relational Thinking](https://i.ytimg.com/vi/99oiRVayRhg/mqdefault.jpg "[Berkeley Seminar] Priyaa Srinivasan: Communicating Relational Thinking
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/")
![[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")
