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Ralph Sarkis (Feb 17 2026 at 09:19):I found this master's thesis on the development of a board game that uses the ideas of universal properties. I didn't fully understand the rules of the game, but I would like to figure them out and try to play if anyone else is interested.
fosco (Feb 17 2026 at 09:47):it looks very cool indeed, and I did not understand the rules either
fosco (Feb 17 2026 at 09:50):as far as I understand I think the game goes sort-of like this: I am the left adjoint, and you have to draw a diagram of type in my category ; vice versa, I have to draw a diagram of type on your category . I have some constructors (e.g. products?) and then I have to "mate" my arrow into yours, using my functorial action and the unit/counit
Ralph Sarkis (Feb 17 2026 at 13:28):What do you mean by "diagram of type "? Do you mean an arrow? I thought you had to construct several arrows that look like a specific shape you are assigned at the beginning.
Matteo Capucci (he/him) (Feb 20 2026 at 16:25):[O]ne of the players says: "The colimits cards can make you go forward, while the limits one pull you back". Although he is a mathematician who does not know anything about category theory, it is quite impressive how he can notice such a thing
It can be played by anyone! :laughing:
Matteo Capucci (he/him) (Feb 20 2026 at 16:31):fosco said:
as far as I understand I think the game goes sort-of like this: I am the left adjoint, and you have to draw a diagram of type in my category ; vice versa, I have to draw a diagram of type on your category . I have some constructors (e.g. products?) and then I have to "mate" my arrow into yours, using my functorial action and the unit/counit
It seems easier, we both play in the same which is the limit/colimit completion of two arrows (the initial moves). The 'game' is the iterative construction of , with the additional mechanics that every time a limit or colimit is added, you get to own its universal co/cone and also assign a free dot on the board.
Matteo Capucci (he/him) (Feb 20 2026 at 16:31):It's not very clear who the initial and terminal objects are
Matteo Capucci (he/him) (Feb 20 2026 at 16:34):Oh I now see there are two games in the thesis :thinking:
Ralph Sarkis (Feb 20 2026 at 17:56):Yes, Section 4.3 has the final game rules, but it kinda assumes you read the previous game rules which makes it harder to understand.