Characterize simplicial maps that lift to homomorphisms of simple games
Determine necessary and sufficient conditions under which a simplicial map between simplicial complexes (viewed as complexes of losing coalitions) extends to a homomorphism between the corresponding simple games, thereby characterizing the class of simplicial maps that lift to game homomorphisms.
References
An interesting question, therefore, is to characterize those simplicial maps which extend to homomorphisms of simple games.
— The topology of simple games
(Volic et al., 16 Mar 2025) in Section 4