Usually vertices of a commutative diagram are labeled with objects like $A\overset{f}{\leftrightarrow} B$.
But now I want to distinguish between vertices of the diagram even if they happen to correspond to the same object.
So I want to draw a diagram like $A\overset{f}{\leftrightarrow} A$ as $0\overset{f}{\leftrightarrow} 1$ where $0$ and $1$ are numbers labeling quiver vertices.
But the notation like $0\overset{f}{\leftrightarrow} 1$ is already reserved for objects $0$ and $1$ not for the numbers labeling diagram vertices.
Please advise which notation to use for both:
- express my idea
- be non-contradictory
- agree (if possible) with customary notation for commutative diagrams.
Hm, well, maybe use different colors for objects of the category in which I draw the diagram and for vertex numbers? Any other ideas?