Abstract circumlocution

Let’s start with 1, then go little less abstract (Conceptual Mathematics, page 81) to a set with one element 1 = {.}, then go more abstract to a terminal object (a set to which there is one function from each set), then furthermore to objects satisfying universal mapping properties (for each object, there is one map from the object to an object satisfying universal mapping properties), then tone it down [or up?] to an object of maps f: A -> B from object A to object B, and finally go back all out abstract to its size: |B| ^ |A|, a number.

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