Dear Neil, Thank you for your message. Yes, I came across your paper about using comonads to present categories at some point, although, I can't quite pin it down to which paper it was. I've been meaning to understand the relationship of containers with our work on game comonads, so maybe I should have a look again. Game comonads (introduced by Abramsky and Dawar) came from an investigation of weak fragments of logics (those fragments where compactness fails) since for these usual methods of categorical model theory cannot be applied. In some sense, game comonads play the role of resource-sensitive categorical model theory, with the resources being e.g. the number of used variables or nesting of quantifiers. Best wishes, Tomas PS: Apologies for my late response. In my limited time during my vacation I had to prioritize responding to the influx of inquiries about the positions. On 8/13/26 07:27, Neil Ghani via Categories wrote:

Hi Tomas

Have you seen presentations of comonads over polynomial funcotrs as directed containers which also gives you, simultaneously, presentations of categories.

All the best Neil

On Wed, Aug 12, 2026 at 8:18 AM Tomáš Jakl via Categories <categories- list@categories.org.au <mailto:categories-list@categories.org.au>> wrote:

Dear All,

I'm looking for a postdoc and PhD student to work with me on the study of both the theory and applications of comonads. We aim to build the theory of presentations of comonads to be able to specify computational resources in a principal way. Therefore, the project is in the intersections of category theory, linear type theory, programming language semantics and potentially also finite model theory (via game comonads), theory of concurrency and so on.

For details, see https://tomas.jakl.one/projects/unicator <https:// tomas.jakl.one/projects/unicator>

Feel free to pass my announcement to potential candidates, should you know any.

Thank you, Tomas _______________________________________________ Categories mailing list -- categories-list@categories.org.au <mailto:categories-list@categories.org.au> To unsubscribe send an email to categories-list- leave@categories.org.au <mailto:categories-list-leave@categories.org.au>

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Kodamai Ltd

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