2-categories and two categories
Actually I think there is an audible difference between the way native speakers of English (of whatever dialect) pronounce 2-categories and two categories, just as there is a subtle difference between the way the White House (the American presidential mansion), the white house (a residence of like color) and even the White house (where the White family reside) are pronounced. The phenomenon is called a "superfix" by linguists. (And once again, categorist in their idle moments show linguistics to be their favorite hobby.) Best Thoughts to all, David Yetter
on being made to think that hard, I guess I do detect a difference \in my syllabic emPHAsis but in the movie I'm not even sure of the word preceding 2!! .oooO Jim Stasheff jds@math.unc.edu (UNC) Math-UNC (919)-962-9607 \ ( Chapel Hill NC FAX:(919)-962-2568 \*) 27599-3250 http://www.math.unc.edu/Faculty/jds On Tue, 1 Jan 2002, David Yetter wrote:
Actually I think there is an audible difference between the way native speakers of English (of whatever dialect) pronounce 2-categories and two categories, just as there is a subtle difference between the way the White House (the American presidential mansion), the white house (a residence of like color) and even the White house (where the White family reside) are pronounced.
The phenomenon is called a "superfix" by linguists. (And once again, categorist in their idle moments show linguistics to be their favorite hobby.)
Best Thoughts to all, David Yetter
Dear Category Theory list, I would like to know if anyone has any references regarding the use of the computation of Kan extensions as a model of computation (e.g. how powerful is some given algorithm as compared to a Turing machine). I have seen the Walters-Carmody algorithm in 'Categories and Computer Science', but there is no mention there of the computational power of the algorithm presented. Any information would be welcome. Yours, -- Robert Byrne 23-Jan-2002 08:39:46 -0400,4207;000000000001-00000000
reply to r.brown@bangor.ac.uk Robert There is a paper R. Brown and Anne Heyworth, `Using rewriting systems to compute left Kan extensions and induced actions of categories', J. Symbolic Computation 29 (2000) 5-31. which does not answer your question on power but instead shows that the Knuth-Bendix process for computing complete rewrite systems for presentations of monoids can be extended to `presentations of Kan extensions'. The method seems different from that of Carmody-Walters, but was inspired by it. See Anne's home page at Leicester for more papers in this area. The `power' of the K-B method is improved since it applies to more examples. Ronnie Brown ----- Original Message ----- From: "Robert Byrne" <rbyrne3@cs.tcd.ie> To: <categories@mta.ca> Sent: Monday, January 21, 2002 12:58 PM Subject: categories: Kan extensions
Dear Category Theory list,
I would like to know if anyone has any references regarding the use of the computation of Kan extensions as a model of computation (e.g. how powerful is some given algorithm as compared to a Turing machine). I have seen the Walters-Carmody algorithm in 'Categories and Computer Science', but there is no mention there of the computational power of the algorithm presented.
Any information would be welcome.
Yours,
-- Robert Byrne
23-Jan-2002 08:45:04 -0400,5395;000000000000-00000000
participants (4)
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David Yetter -
JAMES STASHEFF -
Robert Byrne -
Ronald Brown