This is a crosspost of this question from MSE.
Paulo Aluffi's Book, Algebra, Chapter 0 aims to teach basic algebra from a categorical viewpoint. The first chapters of the book, however, introduce groups and rings using only very basic categorical concepts (no general limits or adjoints). Is there a book which teaches algebra from a more advanced categorical point of view, in particular using general limits and adjoints? Is there a book which teaches algebra from the $n$POV?