nLab simplicial topological space

Contents

Context

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Contents

Definition

A simplicial topological space is a simplicial object in Top.

Often this is called just a simplicial space , if the context is clear.

A special case is that of simplicial manifolds.

Often one is interested in simplicial topological spaces with extra nice properties. See nice simplicial topological space for more on that.

Applications

As with simplicial objects in general, simplicial spaces may serve to model internal ∞-groupoids in Top. Notably there is a rich theory of simplicial topological groups.

References

A standard textbook reference is chapter 11 of

Last revised on June 25, 2021 at 14:09:09. See the history of this page for a list of all contributions to it.