2017/04/09 by Clément Alleaume, Alleaume, Clément · 1 citation
Mathematics · #18D05 #68Q42 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1704.02623
openalex publication_date 2017/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce two applications of polygraphs to categorification problems. We compute first, from a coherent presentation of an n-category, a coherent presentation of its Karoubi envelope. For this, we extend the construction of Karoubi envelope to n-polygraphs and linear (n,n-1)-polygraphs. The second problem treated in this paper is the construction of Grothendieck decategorifications for (n,n-1)-polygraphs. This construction yields a rewriting system presenting for example algebras categorified by a linear monoidal category. We finally link quasi-convergence of such rewriting systems to the uniqueness of direct sum decompositions for linear (n-1,n-1)-categories.