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In mathematics, an isomorphism class is a collection of mathematical objects which are isomorphic to each other.[1]

Isomorphism classes are considered to specify that the difference between two mathematical objects is considered irrelevant.

Definition in category theory

Isomorphisms and isomorphism classes can be formalized in great generality using the language of category theory. Let be a category. A morphism is called an isomorphism if there is a morphism such that and . Consider the equivalence relation that regards two objects as related if there is an isomorphism between them. The equivalence classes of this equivalence relation are called isomorphism classes.


Examples of isomorphism classes are plentiful in mathematics.

However, there are circumstances in which the isomorphism class of an object conceals vital information about it.


  1. ^ Awodey, Steve (2006). "Isomorphisms". Category theory. Oxford University Press. p. 11. ISBN 9780198568612.