Unitary functor calculus with reality

Abstract

We construct a calculus of functors in the spirit of orthogonal calculus, which is designed to study 'functors with reality' such as the Real classifying space functor,. The calculus produces a Taylor tower, the n-th layer of which is classified by a spectrum with an action of. We further give model categorical considerations, producing a zigzag of Quillen equivalences between spectra with an action of and a model structure on the category of input functors which captures the homotopy theory of the n-th layer of the Taylor tower.