isomorphism in a sentence

Examples

1. It can be shown to be unique up to *-isomorphism.
2. Thus, it is determined only up to canonical isomorphism.
3. Limits like products are only defined up to canonical isomorphism.
4. The notion of isomorphism sheds light on the upper-level classification.
5. However, for many purposes, explicit isomorphisms are unnecessary.
6. Uniqueness up to isomorphism is specified by the universal property.
7. A quasiisomorphism is a chain map that is an isomorphism in homology.
8. Representation theory therefore seeks to classify representations up to isomorphism.
9. The latter notation is especially useful in combination with the currying isomorphism.
10. It is an isomorphism when F is a Q-foliation ."