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.
Keywords: groupoid cardinality, stuff types, (2,1)-categories, factorization systems
2020 MSC: 18A99, 18A22, 18A25, 18A32
Theory and Applications of Categories, Vol. 45, 2026, No. 9, pp 307-331.
Published 2026-02-22.
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