2011/08/18 by Conor Smyth, Smyth, Conor, Jon Woolf +1
Mathematics · #18D10 (primary) #18F20 #53A07 #57Q45 #57R99 #58A35 (secondary) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.CT #math.GT #msc:18D10 #msc:18F20 #msc:53A07 #msc:57Q45 #msc:57R99 #msc:58A35
paper · pdf · doi:10.48550/arxiv.1108.3724
19 pages, 1 figure
arxiv created 2011/08/18 · openalex publication_date 2011/08/18 · arxiv updated 2011/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new notion of `n-category with duals', which we call a Whitney n-category. There are two motivations. The first is that Baez and Dolan's Tangle Hypothesis is (almost) tautological when interpreted as a statement about Whitney categories. The second is that we can functorially construct `fundamental Whitney n-categories' from each smooth stratified space X. These are obtained by considering the homotopy theory of smooth maps into X which are transversal to all strata. This makes concrete another idea of Baez and Dolan's which is that a suitable version of homotopy theory for stratified spaces should allow one to generalise the relationship between spaces and groupoids to one between stratified spaces and categories with duals.