cubical set

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.{{Cite journal |last1=Curien |first1=Pierre-Louis |last2=Livernet |first2=Muriel |last3=Saadia |first3=Gabriel |date=2024 |title=Rigidification of cubical quasicategories |journal=Algebraic & Geometric Topology |volume=24 |issue=5 |pages=2851–2888 |doi=10.2140/agt.2024.24.2851 |arxiv=2211.13679 }}