The extent of a formal concept is the set of objects that fall under it.

In formal concept analysis, a formal concept is a pair $(A, B)$ where $A$ is the extent (objects) and $B$ is the intent (attributes). The extent contains exactly the objects that have all the attributes in the intent, and the intent contains exactly the attributes shared by all the objects in the extent.

If the concept is “papers in the repository,” the extent is the set of files with type: paper. If the concept is “authored, published papers,” the extent is the smaller set of files with type: paper, authors, and status: published.

In a concept lattice, concepts are ordered by extent inclusion: a concept with a larger extent (more objects, fewer defining attributes) is more general and sits higher in the lattice.

The term comes from Ganter & Wille (1999). In the Galois connection on a formal context, the extent is the output of the attributes-to-objects map $B'$.

In the extends/restricts framework: the extent is on the extends side of the adjunction — it is what the concept reaches out to cover.