We define a homotopy (we call it sq-homotopy) associated to the square product of two hypergraphs and provide a necessary condition for two hypergraph homomorphisms being homotopic defined by Shing-Tung Yau et al. Then we prove that the sq-homotopy could be characterized by properties of an exponential hypergraph of type II. Finally, we define a Hom construction, and investigate a connection between the sq-homotopy and the Hom construction from the view of topology.
Zhang et al. (Fri,) studied this question.