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there have been recent edits at partially ordered dagger category. i edited a bit in an attempt to polish.
Tim Porter mentions parially ordered groupoids here. I am not sure why. These are not dagger categories, are they? This should go in another entry then, I suppose?
Perhaps one should have partially ordered category separated from partially ordered dagger category.
@Urs: I do not quite see what you mean. Looking at the definition of dagger cat., it seemed to me that a groupoid gave an example of one. Am I confused?
The type of ordered groupoid that Lawson looks at is the groupoid of partial symmetries of a set. The objects are the subsets of a set X and the morphisms are the bijections. The order relation is about one bijection being the restriction of another.
Doesn't that give an example .... I am not thinking clearly and need another coffee so I may be confused. (Alternatively I may have had too may coffees!!)
I do not quite see what you mean. Looking at the definition of dagger cat., it seemed to me that a groupoid gave an example of one. Am I confused?
I guess you are right, I didn't think about it. Let's just make it clear in the entry what's going on.
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