2025/02/05 by Krista Zehr, Zehr, Krista
Business, Management and Accounting · Computer Science · #Optics and Image Analysis #Digital Image Processing Techniques #Computability, Logic, AI Algorithms
paper · pdf · doi:10.48550/arxiv.2502.03585
Groupoid cardinality is an invariant of locally finite groupoids which has many of the properties of the cardinality of finite sets, but which takes values in all non-negative real numbers, and accounts for the morphisms of a groupoid. Several results on groupoid cardinality are proved, analogous to the relationship between cardinality of finite sets and i.e. injective or surjective functions. We also generalize to a broad class of (2,1)-categories a famous theorem of Lovász which characterizes the isomorphism type of relational structures by counting the number of homomorphisms into them.