# nLab intersection

category theory

## Applications

#### Limits and colimits

limits and colimits

# Contents

## Definition

An intersection is a meet of subsets or (more generally) subobjects.

The dual notion is that of union/join.

This includes the traditional set-theoretic intersection of subsets of some ambient set, as well as intersections of completely arbitrary sets (which are subsets of the universe) in material set theory.

In a finitely complete category, the intersection of two monomorphisms $A\hookrightarrow X$ and $B\hookrightarrow X$ can be computed by a pullback of the cospan $A\to X \leftarrow B$.

The nullary intersection of the subsets of $X$ is $X$ itself. A binary intersection is the intersection of two sets, and a finitary intersection is the intersection of finitely many sets. Finitary intersections may be built out of binary and nullary intersections.

Revised on May 31, 2014 07:37:59 by Urs Schreiber (89.204.135.200)