I am trying to apply category theory for knowledge representation and I have concluded that the same class of objects can be endowed with the different sets of morphisms, e.g., arrows that belong to the categories C, D, E etc. Is there research that consider such connected categories C, D and what theorems can be deduced?

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    $\begingroup$ The only relevant property of a "class of objects" is its cardinality. Either I'm missing your point or there is nothing really meaningful to be said. $\endgroup$ – Hurkyl Oct 28 '16 at 10:11

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