Hi,
Is it possible to use category to 'combine' models.
I have seen examples of morphisms being used to show a correspondence
between models.
For example, consider modelling a real world bookshelf. The position
of books on a shelf can include the concept of one book being
'immediately right of' another book. This could be modelled by mapping
the book world concept of 'immediately right of' on to an integer
world where 'immediately right of' could be defined as a Boolean
function:
ImmediatelyRightOf(CurrentBookPosition, OtherBookPosition) ==
(CurrentBookPosition = OtherBookPosition-1).
This example involves expressing the same idea in two models. The
question I am asking is :
�can category theory be used to combine diverse ideas in a unified way
into a single model �
For example, assuming that there exists some reasonable model of space
and some reasonable model of time, can they be formally 'combined'
using category to produce a unified consistent spatio-temporal. Just
allowing the data and operations from both models does not really
address the issues, I need a stronger 'typed system'.
What sort of formalisms should I investigate.
Any assistance appreciated.
I will supply more detail if required.
Regards,
Category Theory Novice
Pat Browne