2011/11/28 by Shantanu Dave, Dave, Shantanu, Michael Kunzinger +1
Mathematics · #58J40 (Primary) 58J47 #58J42 (Secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1111.6570
openalex publication_date 2011/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a (bi)category \mathfrakSing whose objects can be functorially assigned spaces of distributions and generalized functions. In addition, these spaces of distributions and generalized functions possess intrinsic notions of regularity and singularity analogous to usual Schwartz distributions on manifolds. The objects in this category can be obtained from smooth manifolds, noncommutative spaces, or Lie groupoids. An application of these structures relates the longitudinal propagation of singularities for pseudo-differential operators on a groupoid with propagation of singularities on the base manifold.