turkmath.org

Given a discrete group G, there is a classifying space BG whose homotopy type is uniquely determined by the group G. The cohomology of the group G is defined to be the cohomology of the space BG. As a generalization of this, the classifying space BC is defined for a small category C as a simplicial set, and the cohomology of the category C is defined to be the cohomology of BC. I will talk about some open problems related to the cohomology of small categories coming from the representation theory of finite groups.