  In this work, we are concerned with hierarchically hyperbolic spaces and
hierarchically hyperbolic groups. Our main result is a wide generalization of a
combination theorem of Behrstock, Hagen, and Sisto. In particular, as a
consequence, we show that any finite graph product of hierarchically hyperbolic
groups is again a hierarchically hyperbolic group, thereby answering a question
posed by Behrstock, Hagen, and Sisto. In order to operate in such a general
setting, we establish a number of structural results for hierarchically
hyperbolic spaces and hieromorphisms (that is, morphisms between such spaces),
and we introduce two new notions for hierarchical hyperbolicity, that is
concreteness and the intersection property, proving that they are satisfied in
all known examples.
