Localization of $(\infty, 1)$-categories and spectral sequences

TL;DR

This paper introduces two localization methods for $( abla, 1)$-categories that help compute the stages of homotopy spectral sequences for (co)simplicial objects.

Contribution

It presents novel localization techniques for $( abla, 1)$-categories, advancing the understanding of spectral sequence computations.

Findings

Two localization methods for $( abla, 1)$-categories are described.

These localizations determine the successive terms of homotopy spectral sequences.

The approach aids in analyzing (co)simplicial objects in higher category theory.

Abstract

We describe two types of localization for $(\infty, 1)$-categories which determine the successive terms in the homotopy spectral sequence of a (co)simplicial object.