Objects of categories as complex numbers |
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| Authors: | Marcelo Fiore Tom Leinster |
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| Institution: | a Computer Laboratory, University of Cambridge, 15 JJ Thomson Avenue, Cambridge CB3 0FD, UK;b Department of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW, UK |
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| Abstract: | In many everyday categories (sets, spaces, modules, etc.) 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. |
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| Keywords: | Category theory Commutative algebra Rings and algebras |
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