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Author ORCID Identifier
Date Available
7-29-2026
Year of Publication
2026
Document Type
Doctoral Dissertation
Degree Name
Doctor of Philosophy (PhD)
College
Arts and Sciences
Department/School/Program
Mathematics
Faculty
Kate Ponto
Faculty
Bertrand J. Guillou
Abstract
Möbius inversion is a well-studied computational tool in number theory and combinatorics, but it exhibits a pattern which may be familiar to those who study categorical traces. In 2016, Kate Ponto and Michael Shulman characterized duality and traces in the bicategory of profunctors for a particularly nice class of one-cells. We extend these results. Consequently, we construct, for a given poset, a profunctor whose Euler characteristic is the Möbius function of said poset. In light of this, we propose a categorical notion of Möbius inversion.
Digital Object Identifier (DOI)
https://doi.org/10.13023/etd.2026.365
Archival?
Archival
Recommended Citation
Kochmaan, Isaac B., "Understanding Möbius Inversion as Composite of Dual Pairs" (2026). Theses and Dissertations--Mathematics. 134.
https://uknowledge.uky.edu/math_etds/134
