Aderemi Kuku: Cohomology for generalised Bredon coefficient systems and higher K-theory

Let C be a generalised based category (to be defined) and R a commutative ring with identity. In this talk, we construct a cohomology theory in the category B_R(C) of contravariant functors from C to the category of R-modules in an axiomatic way, This cohomology theory generalises simultaneously Bredon cohomology involving finite, profinite, and discrete groups. We also study higher K-theory of the categories of finitely generated projective objects and and finitely generated objects in B_R(C) and obtain some finiteness and other results.