We show that certain diagrams of $\infty$-logoses are reconstructed in homotopy type theory extended with some lex, accessible modalities, which enables us to use plain homotopy type theory to reason about not only a single $\infty$-logos but also a diagram of $\infty$-logoses. This also provides a higher dimensional version of Sterling's synthetic Tait computability -- a type theory for higher dimensional logical relations.

@article{paperbot4013,
  title = {Homotopy type theory as a language for diagrams of $\infty$-logoses},
  author = {Taichi Uemura},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 22, Issue 1},
  year = {2026},
  doi = {10.46298/lmcs-22(1:25)2026}
}