Localizations, colocalizations and non additive *-objects

TL;DR

This paper explores how adjoint functors induce equivalences between subcategories, providing characterizations and applications such as cellular approximations and defining non-additive *-objects.

Contribution

It offers new characterizations of subcategories induced by adjoint functors and introduces the concept of (weak) *-objects in non-additive contexts.

Findings

Characterization of subcategories via adjoint functors

Construction methods for cellular approximations

Definition and properties of non-additive *-objects

Abstract

Given a pair of adjoint functors between two arbitrary categories it induces mutually inverse equivalences between the full subcategories of the initial ones, consisting of objects for which the arrows of adjunction are isomorphisms. We investigate some cases in which these subcategories may be better characterized. One application is the construction of cellular approximations. Other is the definition and the characterization of (weak) *-objects in the non additive case.