# Isomorphism

- tags
- Math, Category Theory

**definition**: An isomorphism is a mapping between two mathematical groups which maintains sets and relations of the elements of the groups. If two mathematical objects have an isomorphism this means they are effectively the same objects after all the elements are renamed (through the isomorph mapping). More formally an isomorphism is a bijective morphism.

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### clark2013: Whatever next? Predictive brains, situated agents, and the future of cognitive science

Isomorphism: any mathematical mapping (morphism) which can be inversed through an inverse morphism.