Hom-counting functions, combinatorial categories and related problems
Category Theory
2025-09-23 v2 Group Theory
Rings and Algebras
Abstract
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.
Cite
@article{arxiv.2506.01501,
title = {Hom-counting functions, combinatorial categories and related problems},
author = {Antonio Ceres and Cristina Costoya and Antonio Viruel},
journal= {arXiv preprint arXiv:2506.01501},
year = {2025}
}
Comments
Revised version to add better context and refine the main results in section 4. 20 pages, no figures