Hi @DavidTanzer

My understanding of terminal object is that there is an incoming arrow from all other object of the Category and initial object has an outgoing arrow to all other object of the category

But as per the definition of generalized element, we are saying that there is an outgoing arrow from terminal object to object A.

But at the same time, there would also be an incoming arrow from A to terminal object because of the later property of being a terminal. In that case, wouldn't we end up having an isomorphism between object A and terminal object? Which means that I can replace object A with a morphism between A and terminal object and vice versa