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Only up to isomorphism? Category Theory and the Foundations of Mathematics

Linnebo, Øystein and Pettigrew, Richard (2010) Only up to isomorphism? Category Theory and the Foundations of Mathematics. [Preprint]


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Does category theory provide a foundation for mathematics that is autonomous with respect to the orthodox foundation in a set theory such as ZFC? We distinguish three types of autonomy: logical, conceptual, and justificatory. Focusing on a categorical theory of sets, we argue that a strong case can be made for its logical and conceptual autonomy. Its justificatory autonomy turns on whether the objects of a foundation for mathematics should be specified only up to isomorphism, as is customary in other branches of contemporary mathematics. If such a specification suffices, then a category-theoretical approach will be highly appropriate. But if sets have a richer 'nature' than is preserved under isomorphism, then such an approach will be inadequate.

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Item Type: Preprint
Linnebo, Øystein
Pettigrew, Richard
Keywords: Category theory; Foundations of Mathematics; Structuralism; Set theory; Categorical Set Theory
Subjects: Specific Sciences > Mathematics
Depositing User: Richard Pettigrew
Date Deposited: 09 Jun 2010
Last Modified: 07 Oct 2010 15:19
Item ID: 5392
Subjects: Specific Sciences > Mathematics
Date: January 2010

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