### 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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