  More than 50 years ago Hedetniemi conjectured that the chromatic number of
categorical product of two graphs is equal to the minimum of their chromatic
numbers. This conjecture has received a considerable attention in recent years.
Hedetniemi's conjecture were generalized to hypergraphs by Zhu in 1992.
Hajiabolhassan and Meunier (2016) introduced the first nontrivial lower bound
for the chromatic number of categorical product of general Kneser hypergraphs
and using this lower bound, they verified Zhu's conjecture for some families of
hypergraphs. In this paper, we shall present some colorful type results for the
coloring of categorical product of general Kneser hypergraphs, which generalize
the Hajiabolhassan-Meunier result. Also, we present a new lower bound for the
chromatic number of categorical product of general Kneser hypergraphs which can
be extremely better than the Hajiabolhassan-Meunier lower bound. Using this
lower bound, we enrich the family of hypergraphs satisfying Zhu's conjecture.
