[Note from moderator: A reminder that potential posts containing html are discarded. Thanks, Bob Rosebrugh] Dear moderator: Could you post this message for Greg Meredith, please? ---------- Forwarded message ---------- From: Meredith Gregory <lgreg.meredith@gmail.com> Date: Sun, Dec 28, 2014 at 1:01 PM Subject: Fwd: Internalizing n-cells to (n-1)-cells To: Mike Stay <metaweta@gmail.com> Dear Mike, i'm not sure why, but my email to the categories list is not getting through. Do you think you might be able to post this question on my behalf? i'm writing to ask a question about higher categories motivated from the computer science perspective. A colleague and i have been looking at an analogue of the internalization of morphisms typically associated with Currying. In our setting we're modeling rewrites in various calculi as 2-morphisms, but to prevent rewrites from happening too freely we have to reify certain contexts as 1-morphisms to mark which rewrites are permitted. Essentially, it's a kind of internalization process and is closely connected with work by Leifer, Milner, and Sewell. Now, though, i'm wondering if there has been a more general study of internalization operators taking n-cells to (n-1)-cells. Is there essentially only one kind of internalization process generalizing the exponential object case? Does anyone have any references? Best wishes, --greg ---------- Forwarded message ---------- From: Meredith Gregory <lgreg.meredith@gmail.com> Date: Sun, Dec 28, 2014 at 12:40 PM Subject: Re: Internalizing n-cells to (n-1)-cells To: Tom Leinster <Tom.Leinster@ed.ac.uk> Dear Tom, No worries. Thanks for getting back to me. It appears that this is not only an unanswered question, but an unasked one! ;-) However, given that the 1-cell to 0-cell case, namely exponential objects play such a pivotal role in computing and fairly important roles even in mainstream maths it seems like it might be worthwhile for me to ask it and seek some answers. Best wishes in the New Year, --greg On Sunday, December 28, 2014, Tom Leinster <Tom.Leinster@ed.ac.uk> wrote:
Dear Greg,
I'm sorry, but I don't know anything at all about this, not even any references. Apologies!
Tom
On Sat, 27 Dec 2014, Meredith Gregory wrote:
Dear Tom, i'm writing to ask a question about higher categories motivated from the computer science perspective. A colleague and i have been looking at an analogue of the internalization of morphisms typically associated with Currying. In our setting we're modeling rewrites in various calculi as 2-morphisms, but to prevent rewrites from happening too freely we have to reify certain contexts as 1-morphisms to mark which rewrites are permitted. Essentially, it's a kind of internalization process and is closely connected with work by Leifer, Milner, and Sewell. Now, though, i'm wondering if there has been a study of internalization operators taking n-cells to (n-1)-cells. Is there essentially only one kind of internalization process? Do you have any references?
Best wishes in the New Year,
--greg
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-- L.G. Meredith Managing Partner Biosimilarity LLC 7329 39th Ave SW Seattle, WA 98136 +1 206.650.3740 http://biosimilarity.blogspot.com -- L.G. Meredith Managing Partner Biosimilarity LLC 7329 39th Ave SW Seattle, WA 98136 +1 206.650.3740 http://biosimilarity.blogspot.com -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]