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.