KASS

Representability for Generalized Multicategories

Matt Earnshaw (University of Tartu)

9 October 2026, 13:30 (Estonian local time)
ICT building, room 218

A multicategory has morphisms whose domains are lists of objects. A generalized multicategory has morphisms whose domains have a shape specified by a monad $T$. Many structures in category theory can be seen as $T$-multicategories for an appropriate $T$. Representability concerns the equivalence between structure defined by universal property, and structure defined coherently. Classically, this is Hermida’s equivalence between representable multicategories and monoidal categories. The theory of representability for generalized multicategories allow us to capture many results of this general shape.

I will give a gentle introduction to generalized multicategories in the sense of Cruttwell and Shulman, and to their representability. This includes new results obtained in work-in-progress with Nathanael Arkor, which seeks to bring into existence the long «in preparation» [CS10b].

Semi-quantitative semantics

Vincent Moreau (Tallinn University of Technology)

9 October 2026, 15:00 (Estonian local time)
ICT building, room 218

In this presentation, I present a new model of linear logic where resources are counted “up to 2”. Quite remarkably, this yields a cartesian closed category that is both FinSet-enriched and not well-pointed. This model exhibits a bounded version of quantitative tools of an infinite nature, such as the Taylor expansion of programs, that we aim to apply to higher-order automata theory. It is the first development of this new research programme that we call semi-quantitative semantics. This is joint work with Tito Nguyễn

Override and Update in Restriction Categories

Chad Nester (University of Tartu)

9 October 2026, 15:30 (Estonian local time)
ICT building, room 218

There are not so many interesting binary operations on partial functions. Among them are the override (aka left preferential union) and update operators. While interesting, these operators are somewhat obscure, and haven’t been studied very much. In this talk I will introduce the override and update operators, and discuss my recent work with JS Lemay, in which we study these operators from the perspective of restriction categories.

Loom - a prototype resource theory editor

Paweł Sobociński (Tallinn University of Technology)

9 October 2026, 16:30 (Estonian local time)
ICT building, room 218

For the ARIA project I promised to work on “coarse-graining string diagrams” – i.e. developing principled ways of avoiding the spaghettisation of diagrams as they get large. Some existing techniques for this in the literature include Melliès’s functor boxes and Lobski’s layered theories. In the summer I decided that the most fun way to make progress would be to vibe code a prototype and experiment hands-on with the design space. To keep things grounded in a concrete setting, and since I also like cooking, the main application so far is a recipe editor. Recipes combine some nice underlying maths that has been fleshed out in recent work: they are time graded (Di Lavore and Román, Timing via Pinwheel Double Categories), they are naturally premonoidal with cook attention as the “runtime object” (Román, Sobocinski, String Diagrams for Premonoidal Categories) and they are also graded by partial commutative monoids: e.g. Crema di Mascarpone needs (at least) two bowls! (Earnshaw, Nester, Román, Monoidal Categories Graded by Partial Commutative Monoids). This talk will be a demo of the tool, called Loom, together with a discussion about some “coarse-graining design principles” that are emerging from my experiments.