Objects of Categories as Complex Numbers
Category Theory
2010-02-04 v1 Commutative Algebra
Rings and Algebras
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.
Keywords
Cite
@article{arxiv.math/0212377,
title = {Objects of Categories as Complex Numbers},
author = {Marcelo Fiore and Tom Leinster},
journal= {arXiv preprint arXiv:math/0212377},
year = {2010}
}
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13 pages