You generalize the whole scheme of "probing" in Set to probing in a general category. In Set, a probe of set Y is a mapping from a singleton object {a} to a set Y.

Here we need to generalize from mapping, singleton, and target set.

Mapping becomes morphism.

Target set becomes target object.

What does a singleton set generalize to?

Hint: How can you characterize a singleton set, not by looking inside it and seeing only one element, but only in terms of the graph structure of its relationships (morphisms) with other sets?