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/ ]