Objects of Categories as Complex Numbers
Abstract
In many everyday categories (sets, spaces, modules, ...) objects can be both added and multiplied. The arithmetic of such objects is a challenge because there is usually no subtraction. We prove a family of cases of the following principle: if an arithmetic statement about the objects can be proved by pretending that they are complex numbers, then there also exists an honest proof.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2002
 DOI:
 10.48550/arXiv.math/0212377
 arXiv:
 arXiv:math/0212377
 Bibcode:
 2002math.....12377F
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Commutative Algebra;
 Mathematics  Rings and Algebras
 EPrint:
 13 pages