Re: Category Theory for the Sciences

[Patrik Eklund <peklund@cs.umu.se>]

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


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