2025/11/26 by Nicholas O. Davidson, Davidson, Nicholas, Jonathan R. Kujawa +3 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.2511.21671
Let \mathbbk be a characteristic zero domain. We define and study a diagrammatic monoidal \mathbbk-linear supercategory WebaffA associated to any locally unital Frobenius \mathbbk-superalgebra A. This category can be viewed variously as an affinization of the finite web category WebA previously defined by the authors and Zhu, as a thickening of the degenerate affine wreath product algebras defined by Savage, or as a Frobenius deformation of affine web categories defined by Song and Wang. We show that there is an asymptotically faithful family of functors from WebaffA to the monoidal supercategory of endofunctors of \mathfrakgln(A)-modules for every n ≥ 1, and use this to establish a basis of `decorated double coset diagrams' for morphism spaces in WebaffA. We also define and establish basis results for the cyclotomic quotient category WebΛA associated with a cyclotomic datum Λ.