tag:blogger.com,1999:blog-8794299614316926152.post1147641333118542198..comments2011-03-20T15:09:27.250-07:00Comments on The Footballing Mind: Poker = Tennis: A Categorical Equivalence of GamesFootballingMindnoreply@blogger.comBlogger2125tag:blogger.com,1999:blog-8794299614316926152.post-36881994033665106682011-03-20T15:09:27.250-07:002011-03-20T15:09:27.250-07:00I'm glad you enjoyed the tennis category. It w...I'm glad you enjoyed the tennis category. It was fun for me to think about how it could be as 'rigorous' as possible, and your points about composition and homotopy are what I'm getting at in problems 7 and 9, respectively. <br /><br />I see two solutions to the failure of composition: either your idea, or introduce a "zero morphism" between any two objects that any nonsensical compositions equal. There are other solutions that involve sacrificing objects = players (encoding more information in the object), which make me not like them as much. <br /><br />Your last paragraph is off-topic, so I'll assume it's just your internet signature and not respond. Cheers!FootballingMindhttp://www.blogger.com/profile/16664283861838566231noreply@blogger.comtag:blogger.com,1999:blog-8794299614316926152.post-49566082952125827092011-03-20T12:26:15.010-07:002011-03-20T12:26:15.010-07:00I've been thinking about the tennis category e...I've been thinking about the tennis category example. I like it a lot. Am I correct that you are interested in morphisms only up to homotopy?<br /><br />It seems like the biggest drawback to the overall description is that morphisms don't compose well. For instance, say you want to compose A->B->C, where A and C are different players. It doesn't seem like a well-defined composition to me. Could you maybe have a category for each match? Then I'd like there to be 3 objects, one for each player, and something like a "winning shot" final object. (Or maybe a "lost point" final object.) The downside to this is that you lose the beautiful Yoneda lemma argument for showing when two players are equivalent.<br /><br />Messi is a dog. Long live Ronaldo, soccernet king.loadbearingstudhttp://www.blogger.com/profile/13358999681576330686noreply@blogger.com