Spectral Sequences in $(\infty, 1)$-Categories

TL;DR

This paper discusses the construction of homotopy spectral sequences within $( abla, 1)$-categories, focusing on model-invariant methods for defining differentials in (co)simplicial objects.

Contribution

It introduces a framework for setting up homotopy spectral sequences in $ abla$-categories with a focus on model-invariant differential construction.

Findings

Provides a systematic approach to spectral sequences in $ abla$-categories

Ensures differentials are constructed in a model-invariant way

Facilitates computations in higher category theory

Abstract

We explain how to set up the homotopy spectral sequence of a (co)simplicial object in an $\infty$-category, with an emphasis on how to construct the differentials in a model-invariant manner.