Varieties of Cubical Sets

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10226)


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.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of PhilosophyCarnegie Mellon UniversityPittsburghUSA
  2. 2.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  3. 3.Carnegie Mellon School of Computer SciencePittsburghUSA
  4. 4.Department of Mathematics and Computer ScienceWesleyan UniversityMiddletownUSA

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