Regarding:

F : A -1-1->     -------->     F : A >--> B
F : A -onto->     -------->     F : A -->> B
F : A -1-1-onto->     -------->     F : A >-->> B

Do you have a textbook reference for the new symbols you propose?

The current symbols we use are from Takeuti & Zaring.  The are rendered 
exactly as in the book on the GIF pages.  There are no Unicode symbols for 
them, so we provided a rough approximation (putting the symbol parts in a 
line instead of stacked vertically).

Norm

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