Endomorphisms of the symmetric 2-rig of finite sets

2019/10/19 by Josep Elgueta, Elgueta, Josep · 1 citation
Computer Science · Mathematics · Decision Sciences · #semigroups and automata theory #Rings, Modules, and Algebras #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.1910.08757

Abstract

Let \widehat\mathbbF\mathbbSet be the groupoid of finite sets and bijections between them equipped with the canonical symmetric rig category structure given by the disjoint union and the cartesian product of finite sets. We prove that the category (in fact, groupoid) of endomorphisms of \widehat\mathbbF\mathbbSet is equivalent to the terminal category, thus providing some evidence that \widehat\mathbbF\mathbbSet is the right categorical analog of the commutative rig ℕ of nonnegative integers. This is shown using a particular semistrict skeletal version of \widehat\mathbbF\mathbbSet for which the endomorphisms can be described very explicitly.

Citations

• Non-canonical isomorphisms

Cited by

• The groupoid of finite sets is biinitial in the 2-category of rig\n categories

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