nLab localizer

Idea

Given a category $\mathcal{C}$, by a localizer in $\mathcal{C}$ (or on $\mathcal{C}$) is often meant to be a class $W \subset Mor(\mathcal{C})$ of morphisms in $\mathcal{C}$ such that $(\mathcal{C},W)$ is a category with weak equivalences, intended as the input datum for the (simplicial) localization of $\mathcal{C}$ at $W$. Typically there are some extra conditions imposed on what constitutes a localizer in a given context.

Examples

The term appears for instance in the discussion of Cisinski model structures, see that Cisinski model structure – Localizers.

It also appears as the notion of basic localizers on Cat.

Related concepts

• localizing subcategory

• modelizer