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Wasn’t aware of this page (or I forget). Have added cross-linking with relation between preorders and (0,1)-categories. There is some overlap between the two entries, but maybe it doesn’t hurt.
Shouldn’t the order-theory analogue of a groupoid be an equivalence relation?
groupoids (and dagger categories) are setoids in order theory. The equivalence relation is just the morphisms of the groupoid or dagger category.
One in general should distinguish between a binary endorelation (edge relation in graph theory), and the mathematical structure consisting of the binary endorelation and the carrier set (directed loop graphs in graph theory), just as one would a binary operation and a magma.
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