Uploaded February 2026 | Updated September 2026, 1 week ago
Accompanying code can be found on github:
github.com/ToposInstitute/elaboratorial
Topos Institute
|
[2-torial] Owen tells Tim about elaborators for type theories [2/2]
🔇 TAP TO UNMUTE
![[2-torial] Owen tells Tim about elaborators for type theories [2/2]](https://i.ytimg.com/vi/xQSG_a_uyKk/mqdefault.jpg "[2-torial] Owen tells Tim about elaborators for type theories [2/2]
Accompanying code can be found on github: https://github.com/ToposInstitute/elaboratorial")
![[Berkeley Seminar] Aaron Huntley (Topos Institute) | Generalised coproduct completions](https://i.ytimg.com/vi/xa04dVG4fEs/mqdefault.jpg "[Berkeley Seminar] Aaron Huntley (Topos Institute) | Generalised coproduct completions
Title: Partial functions and other generalised coproduct completions
Abstract: The category of sets and functions is the free coproduct completion of the terminal category. In a double-categorical setting, Evan Patterson defined a new notion of double (co)product and used it to prove that the double category of sets, functions and spans is the free coproduct completion of the terminal double category. In this talk we both generalise and refine this notion. First, we extend Patterson’s original definition to include (co)products in (co)virtual double categories, which can capture examples such as coproducts in Span(C) even when C does not have pullbacks. Second, we isolate finer classes of double (co)products, denoted (L,R)-(co)products, where L and R are certain classes of functions. As an application, we exhibit the double category of sets, functions and partial functions as a free (L,R)-coproduct completion of the terminal double category.
Date: 9/1/2026")
![[Oxford Seminar] Adrián Puerto Aubel | A glance at Petri net theory](https://i.ytimg.com/vi/z5DXdfV8Fw0/mqdefault.jpg "[Oxford Seminar] Adrián Puerto Aubel | A glance at Petri net theory
Oxford Seminar, February 19 2026
Speaker: Adrián Puerto Aubel
Full Title: A glance at Petri net theory
Abstract: Petri nets are formal models of computing well-known for depicting true concurrency. Unlike automata, they overcome the state-space explosion problem by avoiding interleaving semantics. In this talk I will give an overview of the most prominent theoretical developments of more than 50 years of Petri net theory. This will range from the different expressions of formal semantics of these models as marking graphs, unfoldings, or event structures, to an overview of relevant problems defined on them and their complexities, with a particular focus on structural analysis techniques.")
![[DOTS Lectures] 2. More categories of systems](https://i.ytimg.com/vi/zv10Vgl3Shc/mqdefault.jpg "[DOTS Lectures] 2. More categories of systems
Part of a lecture series on the Double Operadic Theory of Systems (DOTS) presented by David Jaz Myers.")
![[2-torial] Owen tells Tim about elaborators for type theories [2/2] @ToposInstitute](https://i.ytimg.com/vi/xQSG_a_uyKk/maxresdefault.jpg)
