Cubical sets and their site

By Marco De Grandis, L. Mauri. Theory and Applications of Categories, 2003

121 citations recorded by the source corpus.

Extended cubical sets (with connections and interchanges) are presheaves on a ground category, the extended cubical site K, corresponding to the (augmented) simplicial site, the category of finite ordinals. We prove here that K has characterisations similar to the classical ones for the simplicial analogue, by generators and relations, or by the existence of a universal symmetric cubical monoid ; in fact, K is the classifying category of a monoidal algebraic theory of such monoids. Analogous results are given for the restricted cubical site I of ordinary cubical sets (just faces and degeneracies) and for the intermediate site J (including connections). We also consider briefly the reversible analogue, !K.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/76210e8fa1302ec884d6cb03d0cc3f3899ea2fdd

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In Geometry and Topology

1. David Pask
2. Aidan Sims
3. Alex Kumjian
4. Ben Steinberg

In Mathematical Physics

1. Aidan Sims
2. David Pask
3. Alex Kumjian
4. Trent Yeend
5. Iain Raeburn
6. A. Rennie
7. Ben Steinberg
8. N. Fowler

Citations in the corpus

• Homology for higher-rank graphs and twisted C*-algebras (2011, background): “We also show in an appendix how our approach connects the theory of k-graphs to the theory of cubical sets discussed in, for example, [5, 13, 14, 15, 19].”
• La catégorie cubique avec connexions est une catégorie test stricte (2009, unknown): “[11] M.”