Bousfield localisation and colocalisation of one-dimensional model structures

TL;DR

This paper explores Bousfield localisation and colocalisation in one-dimensional model categories, emphasizing constructions via transfer methods without relying on Smith's theorem.

Contribution

It provides a novel approach to localisations and colocalisations using only transfer constructions, avoiding Smith's theorem.

Findings

Constructs localisations and colocalisations using transfer methods

Applies to one-dimensional model categories enriched over 0-types

Avoids reliance on Smith's theorem

Abstract

We give an account of Bousfield localisation and colocalisation for one-dimensional model categories---ones enriched over the model category of $0$-types. A distinguishing feature of our treatment is that it builds localisations and colocalisations using only the constructions of projective and injective transfer of model structures along right and left adjoint functors, and without any reference to Smith's theorem.