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 e-prints
- Pub Date:
- December 2002
- DOI:
- arXiv:
- arXiv:math/0212377
- Bibcode:
- 2002math.....12377F
- Keywords:
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- Mathematics - Category Theory;
- Mathematics - Commutative Algebra;
- Mathematics - Rings and Algebras
- E-Print:
- 13 pages