#
nLab
n-category object in an (infinity,1)-category

Contents
### Context

#### Internal $(\infty,1)$-Categories

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

**(∞,1)-category theory**

**Background**

**Basic concepts**

**Universal constructions**

**Local presentation**

**Theorems**

**Extra stuff, structure, properties**

**Models**

# Contents

## Idea

The notion of n-category formulated internal to an ambient (∞,1)-category is supposed to externally be a kind of (∞,n)-category.

For $n =1$ this is a category object in an (∞,1)-category.

A model along these lines for general with the simplex category generalized to the Theta_n category and the ambient $(\infty,1)$-category being ∞Grpd are *Theta_n spaces*.

Another model is that of n-fold complete Segal space objects.

## Definition

For the moment see at *category object in an (infinity,1)-category – n-Categories*

Last revised on October 10, 2014 at 13:17:19.
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