From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8487 Path: news.gmane.org!not-for-mail From: Patrik Eklund Newsgroups: gmane.science.mathematics.categories Subject: Re: Category Theory for the Sciences Date: Fri, 30 Jan 2015 22:32:28 +0200 Message-ID: References: Reply-To: Patrik Eklund NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1422800139 15520 80.91.229.3 (1 Feb 2015 14:15:39 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 1 Feb 2015 14:15:39 +0000 (UTC) To: Categories Original-X-From: majordomo@mlist.mta.ca Sun Feb 01 15:15:39 2015 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.127]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1YHvJK-0001a1-7R for gsmc-categories@m.gmane.org; Sun, 01 Feb 2015 15:15:38 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:34367) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1YHvIk-0000yu-6R; Sun, 01 Feb 2015 10:15:02 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1YHvIi-0006BT-QJ for categories-list@mlist.mta.ca; Sun, 01 Feb 2015 10:15:00 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8487 Archived-At: On 2015-01-29 02:59, Michael Barr wrote: > I wonder what kind of science outside of string theory would find CT > useful. Dear Michael, Years ago I was in touch with you on monad compositions and monads over something else than just Set. Uncertainty modelling has been interesting for us, and monads over monoidal cats are important, because then we can generalize the signature in a useful way. See e.g. http://www.sciencedirect.com/science/article/pii/S0165011413000997 Let me mention "health" and health nomenclatures as an area, not restricting it only to science, where CT is powerful. Health ontology has been "infected" by simplistic things like description logic, which is just a relational view, so CTwise its just the powerset monad over Set. It's awful to see how SNOMED thinks "ontology" in "health ontology" is the same as "ontology" in "web ontology". However, when we really start to investigate the structure e.g. of WHO's (World Health Organization) reference and derived classifications, we find term monad based approaches very useful. Work is still in its infancy, but as Shakespeare's number of lives is seven, we have six to go, and we are approaching childhood, we think. Those of the readers who know a bit of these classifications already know what I am talking about, and for those who don't, let me just mention a simple example on the distinction between "co-morbidity" and "multimorbidity". Setwise speaking it's a set of ICD codes, but since we do not want to drop that "co", we have an (pre)order between those codes. Further, it's a hierarchy, so it requires a "powertype", and I am not convinced HoTT treats these things properly. We believe it requires a "level of signatures" not tried out before. If anyone is interested, I can organize a short virtual presentation over Adobe Connect to explain this "application area". Best, Patrik [For admin and other information see: http://www.mta.ca/~cat-dist/ ]