query: Initial algebra is "unique up to isomorphism"?
positive_passages.docid: 140583
positive_passages.text: What does it mean for something to hold "up to isomorphism"?
negative_passages.docid: 47617
negative_passages.text: Are groups with all the same Hom sets already isomorphic?
negative_passages.docid: 154318
negative_passages.text: Can a field be isomorphic to its subfield?
negative_passages.docid: 146356
negative_passages.text: To prove two sets are isomorphic is it sufficient to find 2 injections or 2 surjections?
negative_passages.docid: 112125
negative_passages.text: In an extension field, is there any difference between the original field and its isomorphic copy in the extension field?
negative_passages.docid: 116168
negative_passages.text: Is $e^x$ the only isomorphism between the groups $(\mathbb{R},+)$ and $(\mathbb{R}_{> 0},*)$?
negative_passages.docid: 30725
negative_passages.text: Why are naturals < modulus equal if congruent? [uniqueness of remainder]
negative_passages.docid: 117187
negative_passages.text: Uniqueness of the involution on a $C^*$-algebra
negative_passages.docid: 23279
negative_passages.text: Group Theory Isomorphism
negative_passages.docid: 28676
negative_passages.text: Is a finite group uniquely determined by the orders of its elements?
negative_passages.docid: 40366
negative_passages.text: What is the meaning of "algebraically indistinguishable"
negative_passages.docid: 86015
negative_passages.text: $\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
negative_passages.docid: 96025
negative_passages.text: Showing there is only one isomorphism between well ordered sets using transfinite induction
negative_passages.docid: 81238
negative_passages.text: Is $O(2)$ really not isomorphic to $SO(2)\times \{-1,1\}$?
negative_passages.docid: 149109
negative_passages.text: Simple proof that GUID is not unique
negative_passages.docid: 26008
negative_passages.text: Why there is a unique empty set?
negative_passages.docid: 78118
negative_passages.text: Algebraically, why is $\mathbb{Z}[i]/(i + 1)$ isomorphic to $\mathbb{Z}_{2}$?