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arXiv:math/0212377math.CT

Objects of Categories as Complex Numbers

Marcelo Fiore, Tom Leinster

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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.

arXiv comments
13 pages
Journal reference
Advances in Mathematics 190 (2005), 264-277
DOI
Subjects
math.CTCategory Theory math.ACCommutative Algebra math.RARings and Algebras

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Linked by 1 identifiable commenter in 1 comment across 1 thread, from Feb 2013 to Feb 2013. Found in 1 HN submission from Apr 2026 to Apr 2026. Open submission discussions.

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  1. The Algebra of Algebraic Data Types 1 comment

    • Does it help if I tell you that types form a semiring[0]? Note that the natural numbers also form a semiring (with 0 as the additive identity and 1 as the multiplicative identity). The natural numbers can be embedded in the semiring of types, but they are a strict subset - there…

      crntaylorView on HNParent context

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