"Natural" labeling of triangles

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The angles of a triangle are (capital) $A,B,C$ and the lengths of the sides are (lower-case) $a,b,c$.

At your mother's knee, you were taught that the side whose length is called (lower-case) $a$ should be opposite the angle labeled $A$.

Is it the case that in the sense of category theory or in some other appropriate precisely definable sense, this particular way of labeling the sides is "natural" and the other five are not?