Comment by lupire
1 year ago
"Canonical" refers largely to the names we give to things, so that we maximize the extent to which an isomorphism maps the object named A in X to the object named A in Y. And also to choosing an isomorphism that embeds in a different isomorphism (of superstructures) that isn't strictly the topic of the current question.
I don't think anyone thinks canonical isomorphisms are mathematically controversial (except some people having fun with studying scenarios where more than one isomorphism is equally canonical, and other meta studies), they are a convenient communication shorthand for avoiding boring details.
I think the original author makes a good case that a) the shorthand approach isn’t going to fly as we formalise b) different mathematicians mean different things by canonical and these details matter when trying to combining results and that therefore 3) it would be better to provide a proper definition of what you’re talking about and give it an unambiguous name.
let me guess: you haven't read the article, have you?
> Please don't comment on whether someone read an article. "Did you even read the article? It mentions that" can be shortened to "The article mentions that".
https://news.ycombinator.com/newsguidelines.html