Another viewpoint on J-spaces

TL;DR

This paper offers a new interpretation of J-spaces using symmetric spectra, enabling the definition of graded endomorphism objects and providing applications in motivic homotopy theory and infinity categories.

Contribution

It introduces a novel perspective on J-spaces via symmetric spectra and extends the concept to graded endomorphisms in a broad context.

Findings

Interpretation of J-spaces through symmetric spectra

Definition of graded endomorphism objects in general settings

Application to motivic E-infinity ring spectra

Abstract

We give an interpretation of J-spaces in terms of symmetric spectra in symmetric sequences. As application we show how one can define graded endomorphism objects in a general situation. As example we discuss the motivic bigraded endomorphisms of a motivic E-infinity ring spectrum. Finally we give an infinity categorical interpretation of our result.