How to describe a category with only two objects by string diagram?

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I'm learning string diagram (self-study).

In wikipedia, it says that

an object is represented by a portion of plane

a 1-cell $f : A → B$ is represented by a vertical segment—called a string—separating the plane in two (the right part corresponding to $A$ and the left one to $B$)

But what if a category $C$ has only two objects $A$ and $B$ and there is no morphism between them?

How to describe this category by string diagram?

Does this means that object A and B will share (overlap) the same portion in string diagram (because there is no string separate them)?

Thanks.