Morphisms
This won't make sense to most people, but I'm just taking notes for myself so I don't forget...
I notice in the Wikipedia entry on Category Theory the following:
"Relations among morphisms (such as fg = h) are often depicted using commutative diagrams, with "points" (corners) representing objects and "arrows" representing morphisms. The influence of commutative diagrams has been such that "arrow" and morphism are now synonymous."
This reminds me of the (recently neglected) idea of compositional statements in OWL. I require some formalism to make composition a viable suggestion, and this may be a starting point.
The problem with this approach is that predicates can't really be considered to be morphisms, as it is possible to repeat them many times on a given subject. (Does this mean that the predicates can't be morhpisms, or just that they can't be monomorphisms?) Still, I wonder how many category theory ideas are portable into RDF? In a moment of meta-meta insanity, I'm left wondering if there is a morphism from category theory to RDF?
1 comment:
I read up on some category and find it interesting how this can be applied to RDF. I am definately not an expert on category theory, so can you let me know if I am on the right track with the following assumptions?
When applied to RDF a category (ontology?) consists of:
A class of objects (properties).
A class of morphisms, defined as a->b; where a is the domain, b is the range and -> is the property
The morphism type is defined by property type (ie. symmetric)..
For example: Declaring that a property (a) is symmetric to another property (b) says that the relationship between (a) and (b) is an ismorphism ?
...
"In a moment of meta-meta insanity, I'm left wondering if there is a morphism from category theory to RDF?"
hehehe. I wonder what kind of morphism it would be? probably not an isomorphism.
Another scary thought: Could these morphisms be defined as RDF in an ontology that describes the relationship between RDF and category theory.
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