Direct limits and inverse limits of Mackey functors

Abstract Let G be a finite group, S the subgroup category of G , and M a Mackey functor on G . For full subcategories G and H of S , we have the direct limit M ⁎ ( G ) and the inverse limit M ⁎ ( H ) of M . In this paper we study relation between the canonical homomorphisms ind : M ⁎ ( G ) → M ( G ) and res : M ( G ) → M ⁎ ( H ) .