# Lovász-Type Theorems and Game Comonads

@article{Dawar2021LovszTypeTA, title={Lov{\'a}sz-Type Theorems and Game Comonads}, author={A. Dawar and Tom'avs Jakl and Luca Reggio}, journal={2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)}, year={2021}, pages={1-13} }

Lovász (1967) showed that two finite relational structures A and B are isomorphic if, and only if, the number of homomorphisms from C to A is the same as the number of homomorphisms from C to B for any finite structure C. Soon after, Pultr (1973) proved a categorical generalisation of this fact. We propose a new categorical formulation, which applies to any locally finite category with pushouts and a proper factorisation system. As special cases of this general theorem, we obtain two variants… Expand

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