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 [6, Question D] 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.

中文翻译：

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分级双曲组的精细组合定理

在这项工作中，我们关注分层双曲空间和分层双曲组。我们的主要结果是Behrstock，Hagen和Sisto组合定理的广泛推广。特别地，因此，我们证明了层次双曲组的任何有限图乘积再次是层次双曲组，从而回答了Behrstock，Hagen和Sisto提出的[6，问题D]。为了在这样的通用设置下运行，我们为层次双曲空间和同级性（即此类空间之间的态射）建立了许多结构结果，并为层次双曲性引入了两个新概念，即具体性和交集特性，证明在所有已知示例中它们都令人满意。