Abstract: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.
From: Krista Zehr [view email]
[v1]
Wed, 5 Feb 2025 20:03:59 UTC (28 KB)
[v2]
Wed, 19 Feb 2025 19:23:51 UTC (29 KB)
[v3]
Tue, 6 May 2025 22:17:21 UTC (29 KB)
[v4]
Wed, 22 Jul 2026 02:31:22 UTC (30 KB)
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