TITLE: Analogies between analogies
QUESTION [24 upvotes]: "A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies."
--Stefan Banach
See also here: Famous mathematical quotes
So, can someone give an example of an analogy between analogies?

REPLY [2 votes]: Quoting Final dialgebras : from categories to allegories, the authors write that, according to Freyd and Scedrov:

Allegories are to binary relations between sets as categories are to
  functions between sets.

Assuming functions between sets can be regarded as analogies between sets, and assuming that relations between sets can also be regarded as analogies between sets, then the above quote is expressing, in a pretty direct way, an analogy between analogies.