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For each of the following statements about an object c, decide if it is equivalent to the statement “c is terminal”. If so, provide a proof, if not, find a category in which they are not.
The object c has a unique global element.
There exists another object d for which there is a unique generalized element of shape d in c.
For all objects d, there is a unique generalized element of each shape d in c
It seems 2 and 3 are straightforward, but 1 got me totally confused. To avoid spoilers - any hints to get started?
(To be clear - I am trying something out but got confused because what I currently have doesn't match my intuition)