Enumerating Properties of Categories

Abstract

I define categories in first-order logic, enumerate unique categories of *n* arrows, and then enumerate possible properties of a category as statements in the first-order theory of categories, by assigning each one a Gödel numbering. I then show which of the enumerated categories fulfills which of the enumerated properties, and calculate a complexity bound to estimate what realistic number of categories could be studied in this way. I conclude with speculations about development in new directions: higher order properties, or higher order enumeration algorithms.

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