# nLab regular (infinity,1)-category

Contents

### Context

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

(∞,1)-category theory

# Contents

## Idea

A regular $(\infty,1)$-category is the analog of a regular category for (∞,1)-category theory.

## Definition

###### Definition

Let $\mathcal{C}$ be an (∞,1)-category. This is called an exact $(\infty,1)$-category if

1. $\mathcal{C}$ has a terminal object and homotopy fiber products;

2. $\mathcal{C}$ admits a factorization system $(S_L,S_R)$, where $S_L$ is the collection of regular n-connected morphisms and $S_R$ is the collection of n-truncated morphisms.

Last revised on May 17, 2021 at 01:45:25. See the history of this page for a list of all contributions to it.