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removing old query box:
Old discussion:
+–{: .query}
Sridhar Ramesh: Is there meant to also be a partial ordering on the objects in addition to those on the Hom-sets? (Without this, I cannot make sense of the source and target maps preserving the partial order. Indeed, as it stands, I don’t see how this definition is any different from that of a locally partially ordered category.)
David Roberts: I agree: the first definition is of a category enriched in Pos, whereas the reference to source and target maps clearly talks about an internal category. I’ve edited it.
=–
Anonymous
There are the articles 2-poset and dagger 2-poset, which seems to be talking about the same structures as “locally partially ordered category and dagger-category”.
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