2021/04/23 by James Fullwood, Fullwood, James
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Category Theory (math.CT) #Combinatorics (math.CO) #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2104.11399
openalex publication_date 2021/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Groupoids graded by the groupoid of bijections between finite sets admit generating functions which encode the groupoid cardinalities of their graded components. As suggested in the work of Baez and Dolan, we use analytic continuation of such generating functions to define a complex-valued cardinality for groupoids whose usual groupoid cardinality diverges. The complex nature of such a cardinality invariant is shown to reflect a recursion of structure which we refer to as `nested equivalence'.