Higher order track categories and the algebra of higher order cohomology operations

TL;DR

This paper introduces higher order track categories to study the algebraic structure of higher cohomology operations, aiding in the computation of differentials in the Adams spectral sequence.

Contribution

It proposes the notion of n-th order track categories, connecting higher cohomology operations with spectral sequence differentials and Toda brackets.

Findings

Defined n-th order track categories for higher cohomology operations

Connected higher order track categories to spectral sequence differentials

Provided examples including topological and differential algebra-based categories

Abstract

We describe a conjecture on the algebra of higher cohomology operations which leads to the computations of the differentials in the Adams spectral sequence. For this we introduce the notion of an n-th order track category which is suitable to study higher order Toda brackets and the differentials in spectral sequences. We describe various examples of higher order track categories which are topological, in particular the track category of higher cohomology operations. Also differential algebras give rise to higher order track categories.