I've seen it first while studying about dual spaces. A canonical isomorphism between a vector space and its double dual. I've been searching for a while in a little bit more advanced-topic books likes algebraic structures, category theory and representation theory for a formal definition. They are using a LOT the word "canonical", but I couldn't see any record of it in any of those books. How come it is so "hard" for the writer to define the word he used so much? I mean, you probably can find any definition you want in a book just by finding the first time it's been used - this will probably be the definition. Why is it so comfortable to use the word "canonical" so much without any formal definition?