2016/08/15 by Joseph Gubeladze, Gubeladze, Joseph
Mathematics · #18B30 #52A07 #52A25 (Secondary) #52B11 (Primary) #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.1608.04177
openalex publication_date 2016/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Several well known polytopal constuctions are examined from the functorial point of view. A naive analogy between the Billera-Sturmfels fiber polytope and the abelian kernel is disproved by an infinite explicit series of polytopes. A correct functorial formula is provided in terms of the affine-compact kernel. The dual cokernel object is almost always the natural affine projection. The Mond-Smith-van Straten space of sandwiched simplices, useful in stochastic factorizations, leads to a different kind of affine-compact functors and new challenges in polytope theory.