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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)

## Comments

Guess my "intuition" should be called "baseless guessing" - turns out it's much easier to think about this using the category of sets and partial functions.

`Guess my "intuition" should be called "baseless guessing" - turns out it's much easier to think about this using the category of sets and partial functions.`