User talk:RPI
Dear RPJ, Thanks for adding this overview. This is quite useful. I would like to make one remark about the use of the word total. I have always been taught to call total every relation that you call left total. I have been raised to believe that surjective and total are each other's converse. And I have taught the same to generations of students.
Surely it is confusing to find a different meaning of the word total in this (very authoritative) article on wikipedia. Would it hurt to use the word 'complete' instead of 'total'? Then you can substitute 'left-total' back to 'total'. This has the additional advantage that student won't be left wondering why 'surjective' isn't called 'right-total'.