* On reflexivity
@ 1999-03-20 2:19 Tom KRANTZ
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From: Tom KRANTZ @ 1999-03-20 2:19 UTC (permalink / raw)
To: categories
A 'philosophical' interpretation of oriented graphs might be out of
the scope of the categories mailing list, it seems elucidating to me
though.(It could have been for Heraclit and Parmenides.)
I suggest to consider vertices as states and edges as transitions.
A reflexive edge corresponds to a transition from a state to itself.
Two notions of morphism of oriented graphs come seem natural:
- A rigid embedding which preserves difference of states
- A notion of morphism which may equalize different states.
The meaning of equality of states needs precision then.
Coherence semantics deals with a different notion of graph.
This is clear to me and can also be deduced from a discussion between
Thomas Ehrhard and his student Pierre to which I assisted.
This bears an answer to the question of reflexivity I think.
Sincerely, Tom
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