Objects of Categories as Complex Numbers

[varkor]

https://arxiv.org/pdf/math/0212377v1.pdf

https://doi.org/10.1016/j.aim.2004.01.002

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.

Idea

This paper answers the question of when isomorphisms between (certain classes of) types exist when treating types as polynomial equations (extending the results of the well-known paper Seven Trees In One).