Comparing orthogonal calculus and calculus with Reality

We show that there exists a suitable \(C_2\)-fixed points functor from calculus with Reality to the orthogonal calculus of Weiss which recovers orthogonal calculus “up to a shift” in an analogous way with the recovery of real topological K-theory from Atiyah’s K-theory with Reality via appropriate \(C_2\)-fixed points.