Axiomatic representation theory of finite groups by way of groupoids

On the comparison of spans and bisets

We compare the bicategory of spans with that of bisets (a.k.a. bimodules, distributors, profunctors) in the context of finite groupoids. We construct in particular a well-behaved pseudo-functor from spans to bisets. This yields an application to the axiomatic representation theory of finite groups, namely a new proof and a strengthening of Ganter and Nakaoka's identification of Bouc's category of biset functors as a reflective subcategory of global Mackey functors. To this end, we also prove a tensor-monadicity result for linear functor categories.

根群胚与相关李超代数

Root groupoid and related Lie superalgebras

本文提出根群胚概念以替代 Kac-Moody 李超代数中的 Weyl 群，构造并分类相关的根超代数，并通过骨架图建立 Coxeter 性质，推广了经典 Weyl 群理论。