2025/06/02 by Antonio Ceres, Cristina Costoya, Ceres, Antonio +3
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Category Theory (math.CT) #Computability, Logic, AI Algorithms #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2506.01501
openalex publication_date 2025/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Combinatorial categories satisfy a stronger form of Yoneda Lemma, namely, the isomorphism type of an object can be recovered by counting the number of homomorphisms from all other objects into it. In this work, we show that this property holds for sufficiently small categories by studying the algebra of homomorphism-counting functions. We present applications of the results to the isomorphism problem in group, graph and ring theory.