Dugger, DanielRaies, Daniel2019-09-182019-09-182019-09-18https://hdl.handle.net/1794/24925Mackey functors over the group Z/2 are useful in the study of Z/2-equivariant cohomology. In this dissertation we establish results which are useful for homological algebra computations for certain Mackey rings over Z/2. We also provide some Ext computations for Mackey modules over Mackey rings. Additionally, we study the bigraded ring M_2 (which is the Bredon cohomology of a point) and its Mackey ring analog. This includes a computation of Ext(k,k) over M_2 and a computation of Ext(M,k) for certain M_2-modules M as well as a proof that the Mackey ring analog is self-injective as a bigraded Mackey ring.en-USAll Rights Reserved.Bredon CohomologyHomological AlgebraHomotopy TheoryMackey FunctorsElectronic Thesis or Dissertation