Uploaded December 2025 | Updated September 2026, 2 weeks ago
Recorded at the Oxford Office on the 5th of December 2025.
Topos Institute
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[2-torial] David Jaz tells Brendan about a topos-theoretic interpretation for conceptual modelling
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![[2-torial] David Jaz tells Brendan about a topos-theoretic interpretation for conceptual modelling](https://i.ytimg.com/vi/kFQpKp-ehZI/mqdefault.jpg "[2-torial] David Jaz tells Brendan about a topos-theoretic interpretation for conceptual modelling
Recorded at the Oxford Office on the 5th of December 2025.")
![[DOTS Lectures] 1. Categories of systems](https://i.ytimg.com/vi/kZ4muU5Wc_4/mqdefault.jpg "[DOTS Lectures] 1. Categories of systems
Part of a lecture series on the Double Operadic Theory of Systems (DOTS) presented by David Jaz Myers.")
![[Berkeley Seminar] Raph Levien | How Rust won: the quest for performant, reliable software](https://i.ytimg.com/vi/k_-6KI3m31M/mqdefault.jpg "[Berkeley Seminar] Raph Levien | How Rust won: the quest for performant, reliable software
Title: How Rust won: the quest for performant, reliable software
Abstract: For a long time, high performance has been in tension with reliability. In particular, languages designed for high performance were not memory safe, with real implications for unexpected crashes and security vulnerabilities. Rust is the first practical language to address this tension, building on affine types and other principles programming language theory, synthesized with an attention to low level systems programming. Rust’s success emerged not just from a clever idea, but consistently excellent execution and the formation of a strong community around the language. This talk will discuss several aspects of what Rust got right, as well as the rocky journey of ideas from academic theory to real world impact.
Slides: https://docs.google.com/presentation/d/1SoDsm_m_pb_gS6Y98HghhzBviYZxp3F2XawhIppJQQo/edit?usp=sharing
https://topos.institute/events/berkeley-seminar/")
![[DOTS Lectures] 11. A general representability theorem for Systems Theory Pt. 1](https://i.ytimg.com/vi/kpmhI1oHGnM/mqdefault.jpg "[DOTS Lectures] 11. A general representability theorem for Systems Theory Pt. 1
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")
![[TopOx] Steve Awodey: Path Types in Algebraic Type Theory](https://i.ytimg.com/vi/lanvZuki4qQ/mqdefault.jpg "[TopOx] Steve Awodey: Path Types in Algebraic Type Theory
18th of May 2026. Slides available at https://topos.institute/events/topox/
A representable natural transformation u : U* → U in the category Psh(C) of presheaves on a small category C is a “natural model of dependent type theory. The type-forming operations may be described as an algebraic structure on u, representing corresponding operations on the type-families classified by u. For example, the dependent product or “Pi-type” is an algebra structure for the polynomial endofunctor
P_u : Psh(C) → Psh(C) .
Similar operations on u represent the other type-formers of unit type, dependent sums, and identity types. The latter are given by a recently determined “path-type” structure, which relates such models to cubical (Quillen) model categories.")
![[DOTS Lectures] 17. Representability for double operad algebras](https://i.ytimg.com/vi/larbRprPuPM/mqdefault.jpg "[DOTS Lectures] 17. Representability for 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")
![[DOTS Lectures] 3. Moore machines](https://i.ytimg.com/vi/m-HDSZ0iNWE/mqdefault.jpg "[DOTS Lectures] 3. Moore machines
Part of a lecture series on the Double Operadic Theory of Systems (DOTS) presented by David Jaz Myers.")
![[2-torial] Toposes: from topological spaces to databases](https://i.ytimg.com/vi/mNFibqlr_Bk/mqdefault.jpg "[2-torial] Toposes: from topological spaces to databases
[2-torial] Toposes: from topological spaces to databases")
![[Berkeley Seminar] Evan Patterson | A uniform type theory for internal languages of cat. structures](https://i.ytimg.com/vi/mknZxNcn0Ho/mqdefault.jpg "[Berkeley Seminar] Evan Patterson | A uniform type theory for internal languages of cat. structures
Title: A uniform type theory for internal languages of categorical structures
Abstract: A hallmark of categorical logic is the interplay between category theory and type theory. A categorical structure can provide the semantics of a type theory; in the other direction, type theory can be used to describe the internal language of a categorical structure. The internal language is an ergonomic notation, based on elements and function application, to specify morphisms in the category. Typically, discovering an internal language is a bespoke process, performed anew for each categorical structure of interest. In this talk, we propose a uniform type theory giving internal languages for much of the “substructural” hierarchy of categorical logic, including such structures as categories, multicategories (planar, symmetric, and cartesian), PROPs, Lawvere theories, (symmetric) monoidal categories, cartesian categories, and Markov categories. The framework builds on the speaker’s work in double-categorical logic, and is described in preliminary form at: https://next.catcolab.org/rfc/0004
Date: May 26, 2026")
![[Oxford Seminar] Matteo Capucci | 2-classifiers for 2-algebras](https://i.ytimg.com/vi/mpHnD7peDS8/mqdefault.jpg "[Oxford Seminar] Matteo Capucci | 2-classifiers for 2-algebras
Oxford Seminar, 26th of June 2025
In this talk I will report on work in progress, joint with David Jaz Myers, about lifting discrete opfibration classifiers (2-classifiers, i.e. a Set-like object) from a 2-category K to the 2-category of algebras of a 2-monad T. In the setting of DOTS, we often construct behaviour functors as representables, but without a 2-classifier one cant really call these representables. Moreover, there is a strong connection between compositionality of such functors, the properties of the algebra they map out of, and the properties of the object(s) that represents them. These phenomena are in fact completely general, so we set out to better understand the situation and found some frankly interesting notions and results, chiefly a tight result on the existence of 2-classifiers for 2-algebras.")
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