| 41. | It can be shown to be unique up to *-isomorphism.
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| 42. | Thus, it is determined only up to canonical isomorphism.
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| 43. | Limits like products are only defined up to canonical isomorphism.
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| 44. | The notion of isomorphism sheds light on the upper-level classification.
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| 45. | However, for many purposes, explicit isomorphisms are unnecessary.
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| 46. | Uniqueness up to isomorphism is specified by the universal property.
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| 47. | A quasiisomorphism is a chain map that is an isomorphism in homology.
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| 48. | Representation theory therefore seeks to classify representations up to isomorphism.
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| 49. | The latter notation is especially useful in combination with the currying isomorphism.
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| 50. | It is an isomorphism when F is a Q-foliation ."
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