# nLab relative (∞,1)-limit

Contents

### Context

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

(∞,1)-category theory

## Models

#### Limits and colimits

limits and colimits

# Contents

## Idea

The relative version of the notion of (∞,1)-limit.

## Definition

###### Definition

For $f \colon \mathcal{C} \to \mathcal{D}$ an (∞,1)-functor between (∞,1)-categories which is presented by an inner fibration of quasi-categories (which we denote by the same symbols), and for

$\overline{p} \colon K^{\ast} \to \mathcal{C}$

a cocone diagram in $\mathcal{C}$ over the $K$-shaped diagram

$p \coloneqq \overline{p}|K \,,$

then $\overline{p}$ is an $(\infty,1)$-colimiting cocone if the canonical map

$\mathcal{C}_{\overline{p}/} \to \mathcal{C}_{p/} \underset{\mathcal{D}_{f p /}}{\times} \mathcal{D}_{f\overline{p}/}$

(from the co-slice quasi-category) is an acyclic Kan fibration of simplicial sets.

## References

Created on June 11, 2013 at 12:00:34. See the history of this page for a list of all contributions to it.