I think Category Theory is really interesting in the way it frames the human endeavor of trying to understand and map phenomena out and then reason about it, but it is a super abstract thing by design... but the thought came to me that the deluge of modern board game designs with many that are carefully designed to have complex interactions and mechanics might be a place that the utility of Category Theory could be explained in an approachable way (at least to board game nerds...) that also demonstrated the basic utility of it as a way to examine different complex systems and compare them in some logically precise way.

https://en.wikipedia.org/wiki/Category_theory

To put it succinctly, could we look at Dominion and examine whether other Deckbuilding games are Isomorphic or are in some sense fundamentally similar or dissimilar in some way that isn't just qualitative? Certainly we can say that a "Bag builder" like Orléans or Quacks Of Quedlinburg can be equivalent mechanically to a Deckbuilder but what about more nuanced less obvious questions of similarity?

https://boardgamegeek.com/boardgame/36218/dominion

https://boardgamegeek.com/boardgamemechanic/2664/deck-bag-and-pool-building

It seems to me it would give a language to talking analytically about game design, it could express things like whether you could tweak a Dominion game with certain market cards to approximate the same mechanics as another Deckbuilding game or whether there are fundamental differences between Dominion and the other Deckbuilder that preclude that and if so how precisely so does that manifest?

I realize Category Theory isn't quite Science... but it certainly represents a scientific approach to representing how we categorize and analyze the universe so in that sense... I don't know it felt right to ask it here... but I can re-post on a math community if it doesn't fit here if wanted?

https://www.math3ma.com/blog/what-is-category-theory-anyway