Algebraic models for functor calculus

There is a striking and useful analogy between equivariant homotopy theory and functor calculus. In the equivariant setting, Greenlees conjectured that the category of rational G-spectra has an algebraic model - meaning it is equivalent to the derived category of an abelian category with desirable finiteness properties. This talk will examine the functor calculus counterpart of this conjecture in (potentially) more than one flavour of functor calculus. (Joint work with D. Barnes and M. Kedziorek.)