Varieties of Cubical Sets
Category Theory
2017-04-20 v2 Logic in Computer Science
Algebraic Topology
Logic
Abstract
We define a variety of notions of cubical sets, based on sites organized using substructural algebraic theories presenting PRO(P)s or Lawvere theories. We prove that all our sites are test categories in the sense of Grothendieck, meaning that the corresponding presheaf categories of cubical sets model classical homotopy theory. We delineate exactly which ones are even strict test categories, meaning that products of cubical sets correspond to products of homotopy types.
Cite
@article{arxiv.1701.08189,
title = {Varieties of Cubical Sets},
author = {Ulrik Buchholtz and Edward Morehouse},
journal= {arXiv preprint arXiv:1701.08189},
year = {2017}
}
Comments
16 pages; to appear in proceedings of RAMiCS 2017