# nLab solidification functor

### Context

#### $(\infty,1)$-Category theory

(∞,1)-category theory

Background

Basic concepts

Universal constructions

Local presentation

Theorems

Extra stuff, structure, properties

Models

#### Stable homotopy theory

stable homotopy theory

Introduction

# Contents

#### Higher category theory

higher category theory

## 1-categorical presentations

#### Higher algebra

higher algebra

universal algebra

## Idea

Namely, I claim that if you’re willing to pass to suspension spectra, then you do get a fully well-defined functor which takes a CW-complex (viewed as a condensed set) to the suspension spectrum of its associated anima. But now this is not a functor to ordinary spectra, but a functor to condensed spectra which happens to take “discrete” values (discrete in the condensed direction) on CW-complexes.

Actually, what you really have is a colimit-preserving endofunctor of condensed spectra, which when applied to the suspension spectrum of a CW complex (viewed as a condensed set) gives the suspension spectrum of its associated anima. This is the “solidification” functor, which works for spectra much in the same way it works for abelian groups.