# STRUCTURE TO POLYNOMIAL FUNCTORS IN ORTHOGONAL CALCULUS II

### Abstract

The orthogonal calculus of functors is a beautiful tool for calculating the homotopical properties of functors from the category of inner product spaces to pointed spaces or any space enriched over . It splits a functor *F* into a Taylor tower of fibrations, where our *n-th* fibrations will consist of maps from the *n*-polynomial approximation of *F* to the (*n − *1)*− *polynomial approximation of* F*. The homotopy fiber or layer (the difference between *n*-polynomial and (*n − *1)*−* polynomial approximation) of this map is then an *n*-homogeneous functor and is classified by an *O *(*n*)- spectrum up to homotopy which is usually denoted as .This structure is considered in this study

Published

2021-10-17

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Section

ARTICLES