2004/08/23 by Philip J. Higgins, Higgins, Philip J. · 1 citation
Mathematics · #18D05 #18D35 #55U99 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AT #math.CT #msc:18D05 #msc:18D35 #msc:55U99
paper · pdf · doi:10.48550/arxiv.math/0408306
15 pages, xypic
arxiv created 2004/08/23 · openalex publication_date 2004/08/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The relationships between thin elements, commutative shells and connections in cubical omega-categories are explored by a method which does not involve the use of pasting theory or nerves of omega-categories (both of which were previously needed for this purpose; see previous work by Al-Agl/Brown/Steiner. It is shown that composites of commutative shells are commutative and that thin structures are equivalent to appropriate sets of connections; this work extends to all dimensions the results proved in dimensions 2 and 3 by Brown/Mosa, and Brown/Kamps/Porter.