#
nLab

ASSet

### Context

#### Category theory

**category theory**

## Concepts

## Universal constructions

## Theorems

## Extensions

## Applications

#### 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

The category $sSet_+$ of **augmented simplicial sets** is the category of presheaves on the *augmented* version of the simplex category $\Delta_a$:

$sSet_+ := Set^{\Delta^{op}_a}
\,.$

This is the category whose objects are augmented simplicial sets and whose morphisms are the evident morphisms between these.

## Applications

The join of simplicial sets is most naturally defined via a construction on augmented simplicial sets.

Revised on November 4, 2010 08:48:44
by

Urs Schreiber
(87.212.203.135)