Abstract
Given a general finite group G , we consider several categories built on it, their Grothendieck topologies and resulting sheaf categories. For a certain class of transporter categories and their quotients, equipped with atomic topology, we explicitly compute their sheaf categories via sheafification. This enables us to identify G -representations with various fixed-point sheaves. As a consequence, it provides an intrinsic new proof to the equivalence of M. Artin between the category of sheaves on the orbit category and that of group representations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have