Pointed integral coalgebras and R-local homotopy theory

TL;DR

This paper establishes a fully faithful embedding of the homotopy category of Bousfield R-local spaces into a category of simplicial pointed flat coalgebras for a principal ideal domain R.

Contribution

It introduces a new categorical framework connecting R-local spaces with simplicial pointed flat coalgebras, expanding the tools for homotopy theory over principal ideal domains.

Findings

Homotopy category of Bousfield R-local spaces injects into coalgebra category

The embedding is fully faithful, preserving homotopical information

Framework applies to principal ideal domains R

Abstract

We show that, for a principal ideal domain R, the homotopy category of Bousfield R-local spaces injects fully faithful into a homotopy category of simplicial pointed flat coalgebras.