Bruno said > Johnson ? Do you mean Johnstone?

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Yes > ....... > is almost impossible (even if only a familiarity with only the most > basic introduction is enough). Adding "category theory" to that > panel makes things worst as you can imagine. > I can certainly see that. > Actually I have a much more rare and implausible book: an > introductory course in category theory from Kinshasa > University Press (Congo), quite > nice but no more on the market Sounds of value in many ways, especially if in say Wolof or Yoruba I imagine, but I expect it is in French. Most books from the area must carry a "Thus spake Ozymandias" feeling with them, I imagine. I used to like Krio, which is a language which could roughly be described as an English/Yoruba creole. I only speak English. > A good book on Category Theory is the book by Robert Goldblatt > "Topoi". I still have Chu spaces rather than toposes in mind but Gouts used toposes for his MWI, as I mentioned in a FOR post. My understanding is that the two are a bit different. There are a number of posts on the internet about it all, for example http://north.ecc.edu/alsani/ct01(5-8)/msg00051.html and also http://north.ecc.edu/alsani/ct01(5-8)/msg00053.html I am so far puzzled rather than intrigued by any topos/Chu space correspondences as I want to keep it all as simple yet as usable as I can. People who like to delve in quantum theory often seem to go to toposes but I want to avoid QT although of course possibly can't. > The *must* remains the MacLane's book "categories for the working > mathematician" (takes me year to grasp just the preface, though!, > but then I learn a lot). Well I want to only use category theory if I can, so I tried to keep it simple by sticking to Lawvere and Schanuel which apparently experts find a few hours light entertainment but I find thoughtprovoking. . I hope I don't need MacLane but may have to. (Barr & Wells online is what I have and try to avoid, plus a lot of other online stuff, all I can find). > In relation with my work, and oversimplifying a little bit, > categories > appears mainly as generalisation of the modal S4, or S4Grz logics, > and as such correspond to "first person notion"(*) and their > intuitionistic logic. > Contrariwise, the 3-person notions, which with comp are based on > recursion theory, are the notion which fits the less with the category > approach (but with the Combinators some light appears in the dark > ...). > > (*) Kripke models of S4 are multiverse with a reflexive and > transitive relation of accessibility (between > universes/states/observer-moments). > A category is just the same except that more than one arrows are > allowed among the "points/states...", and arrows must be composed. > Sounds as if it could be interesting but I have only a couple of books by Boolos (and perhaps irrelevantly "Forever Undecided" though years ago I did a bit of logic from Smullyan's "Theory of Formal systems" monograph which unfortunately now seems to have gone the way of all good books). ----- Original Message ----- From: "Bruno Marchal" <[EMAIL PROTECTED]> To: "uv" <[EMAIL PROTECTED]> Cc: <everything-list@eskimo.com> Sent: Wednesday, November 09, 2005 3:11 PM Subject: Re: Question for Bruno > > Le 08-nov.-05, à 18:48, uv a écrit : > > > Bruno wrote > > > >> I don't know about the work of Heather and Rossiter, except some > >> thought on quantum computation I just found by Googling. Perhaps you > >> could elaborate a little bit. > > > > I can answer you briefly on that one immediately by giving URL > > http://computing.unn.ac.uk/staff/CGNR1/advstudiesmathsmonism.pdf > > Please let me know if it disappears before you get there, nowadays > > they sometimes do unfortunately. > > > I got it and have printed it. Interesting (especially for the Category > Theory minded people, which I am a little bit) but I do think it is a > little bit out of topic, at least for the moment. In my "Brussels' > thesis" I have use a bit of category theory, but I have decided to > suppress it when I realized that asking referees simultaneous > knowledge in > > basic cognitive science/philosophy of mind, > + mathematical logic > + quantum theory > > is almost impossible (even if only a familiarity with only the most > basic introduction is enough). Adding "category theory" to that panel > makes things worst as you can imagine. > > > > > > > > That is very close to implying a > > TOE. My own group is http://groups.yahoo.com/group/ttj It also > > gives my blog and URL. > > > > Some work has also been done by Heather and Rossiter on quantum > > computing, with some comments on Deutsch's work. > > > > By the way Johnson > > > Johnson ? Do you mean Johnstone? > > > > seems to be the really important man in category > > theory, "Sketching the Elephant" being the big book but afraid I am > > still reading Lawvere and Schanuel > > > > That is a good one. A very rare elementary introduction to category > theory. > Actually I have a much more rare and implausible book: an introductory > course in category theory from Kinshasa University Press (Congo), quite > nice but no more on the market. I have also the notes by Lawvere before > Shanuel makes the book. > I really love category theory (especially for logic and computer > science), and eventually, when I will come back to the combinators (if > I do) category will appears naturally by themselves, but I do think it > could be premature now. > A good book on Category Theory is the book by Robert Goldblatt "Topoi". > Some categorist (like Johnstone) criticize it, because it does not > stick on pure diagrammatic chasing, but then Goldblatt is a (modal) > logician, and actually it is that which makes the book understandable > (at least for logician). > The *must* remains the MacLane's book "categories for the working > mathematician" (takes me year to grasp just the preface, though!, but > then I learn a lot). > > In relation with my work, and oversimplifying a little bit, categories > appears mainly as generalisation of the modal S4, or S4Grz logics, and > as such correspond to "first person notion"(*) and their intuitionistic > logic. > Contrariwise, the 3-person notions, which with comp are based on > recursion theory, are the notion which fits the less with the category > approach (but with the Combinators some light appears in the dark ...). > > (*) Kripke models of S4 are multiverse with a reflexive and transitive > relation of accessibility (between universes/states/observer-moments). > A category is just the same except that more than one arrows are > allowed among the "points/states...", and arrows must be composed. > > Bruno > > http://iridia.ulb.ac.be/~marchal/ >