# nLab lattice object

Contents

category theory

## Applications

#### Limits and colimits

limits and colimits

(0,1)-category

(0,1)-topos

# Contents

## Idea

The notion of a lattice object is the generalization of that of lattice as one passes from the ambient category of sets into more general ambient categories with suitable properties.

## Definition

In a finitely complete category $C$, a lattice object is a bicartesian preordered object that is also a partially ordered object.