title: Whats the meaning of "unique up to isomorphism"?
body: <p>Whats the meaning of "unique up to isomorphism"? To give some context, I came across the phrase <a href="https://en.wikipedia.org/wiki/Initial_algebra#Use_in_computer_science" rel="nofollow">reading about initial algebras</a>.</p>
  
  <p>It seems that <em>up to</em> means "to ignore" (sometimes said as "modulo"). Isomorphism means that the objects are the same in some way (with a bidirectional mapping). However, "unique ignoring that they are the same" still perplexes me.</p>