A combinatorial category [Pultr (1973, Def. 1.7)] is a locally finite category satisfying the unnatural isomorphism property:
Or equivalently
Let be a combinatorial category and let . If and is weakly terminal, then .
For all , we have
Hence we may divide both sides by (which is nonzero since is weakly terminal) and so for all , from which we have .
not related is the notion of combinatorial model category
A. Pultr, Isomorphism types of objects in categories determined by numbers of morphisms, Acta Scientiarum Mathematicarum 35 (1973) 155-160 [pdf]
Luca Reggio?, Polyadic sets and homomorphism counting, Advances in Mathematics 410 (2022): 108712.
Shoma Fujino and Makoto Matsumoto, Lovász’s hom-counting theorem by inclusion-exclusion principle, arXiv:2206.01994 (2022).
Last revised on March 16, 2024 at 12:32:05. See the history of this page for a list of all contributions to it.