My research focus is in Equivariant Algebra: the theory of those algebraic objects which arise from equivariant (stable) homotopy theory. The algebraic objects of chief importance in this theory are Mackey Functors and Tambara Functors, which are equivariant generalizations of Abelian groups and commutative rings, respectively.
Typically, Mackey and Tambara functors are defined with respect to some (finite) group \(G\) which acts on our spaces. However, we can replace the category of finite \(G\)-sets with any locally cartesian closed (LCC) category to obtain more generalized notions of Mackey and Tambara functors. By developing the theory at this level of generality, we actually simplify the exposition and proofs of certain theorems.
[This page is under construction]