In topology, a branch of mathematics, a cubical set is a set-valued contravariant functor on the category of (various) n-cubes. Cubical sets have been often considered as an alternative to simplicial sets in combinatorial topology, including in the early work of Daniel Kan and Jean-Pierre Serre. They have also been developed in computer science, in particular in concurrency theory and in homotopy type theory.
See also Simplicial presheaf
References
nLab, Cubical set. Rick Jardine, Cubical sets, Lecture 12 in "Lectures on simplicial presheaves" https://web.archive.org/web/20110104053206/http://www.math.uwo.ca/~jardine/papers/sPre/index.shtml