Objects of categories as complex numbers
Copyright policy )Objects of categories as complex numbers
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.
13 pages
- University of Glasgow United Kingdom
- University of Cambridge United Kingdom
- Computer Laboratory University of Cambridge United Kingdom
- Arden University United Kingdom
rings and algebras, Mathematics(all), Rings and algebras, Categorical structures, Mathematics - Category Theory, Semirings, Mathematics - Rings and Algebras, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), category theory, Rings and Algebras (math.RA), commutative algebra, FOS: Mathematics, Category Theory (math.CT), Commutative algebra, QA, Category theory
rings and algebras, Mathematics(all), Rings and algebras, Categorical structures, Mathematics - Category Theory, Semirings, Mathematics - Rings and Algebras, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), category theory, Rings and Algebras (math.RA), commutative algebra, FOS: Mathematics, Category Theory (math.CT), Commutative algebra, QA, Category theory
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