What is an example of a thin abelian (or a thin poset) category? Or perhaps such categories cannot exist?
2026-03-28 03:32:57.1774668777
A thin abelian category
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They are the same as complete directed graphs, so they all are equivalent to trivial abelian category.
Since an abelian category admits a zero arrow between any two objects, so that there is at least one arrow between any two objects, and a zero arrow as an endomorphism on any object, every thin abelian category looks like a complete directed graph. Conversely, every complete directed graph admits a trivial structure as an abelian category.