TITLE: Deeper meaning of "canonical"?
QUESTION [5 upvotes]: For years I thought "canonical" for isomorphisms just means something like "obvious", "without arbitrarily choice", "simple" depending on the context, and I accepted the idea that there is no deeper meaning of "canonical" and no clear definition.
Reading about categories I noticed that "canonical" is sometimes used when there's a "natural equivalence" in the language of category theory. So my question: 
Can we clearly define "canonical" by means of category theory in an abstract way, so that the situations when we use "canonical" in our "real" mathematician life are special cases of this abstract situation?

REPLY [2 votes]: IMO, a "canonical map" is one implied by context.
Language and notation is full of shorthand and abbreviations; it's far too cumbersome to say everything. For example, if we have a ring $R$ and an ideal $I$, the quotient is some ring $Q$ together with a surjective map $\pi : R \to Q$ whose kernel is $I$. 
However, the usual language is just say that $Q$ is the quotient, without any mention of $\pi$. Then, if we later need $\pi$, we name it as the "canonical map" $R \to Q$.
I'm not aware of a theory that tries to capture the notion — your best bet on that, I think, would be to go over to cstheory.stackexchange.com and ask if there is a theory underpinning implicit conversions.