nLab bicubical set

Idea

Bicubical set are to cubical sets as bisimplicial sets are to simplicial sets.

References

On synthetic (∞,1)-category theory in cubical type theory with bicubical sets:

• Matthew Weaver, Daniel Licata, A Constructive Model of Directed Univalence in Bicubical Sets, in: Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science. LICS ’20, Association for Computing Machinery (2020) 915–928 [doi:10.1145/3373718.3394794]

Exposition in:

• Matthew Weaver, A Constructive Model of Directed Univalence in Bicubical Sets, talk at HoTTEST (April 2020) [pdf, video]