2009/07/23 by Eugenia Cheng, Cheng, Eugenia, Michael Makkai +1 · 1 citation
Mathematics · #18A05 #18D05 #18D10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.CT #msc:18A05 #msc:18D05 #msc:18D10
paper · pdf · doi:10.48550/arxiv.0907.3961
14 pages, to appear in Cahiers de Topologie et Geometrie Differentielle Categoriques
arxiv created 2009/07/23 · openalex publication_date 2009/07/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that doubly degenerate Penon tricategories give symmetric rather than braided monoidal categories. We prove that Penon tricategories cannot give all tricategories, but we show that a slightly modified version of the definition rectifies the situation. We give the modified definition, using non-reflexive rather than reflexive globular sets, and show that the problem with doubly degenerate tricategories does not arise.