Next, let's lift \\(f_1\\) to a function that operates on a set of objects.

The standard way is to take the union of \\(f_1(o)\\) as \\(o\\) ranges over \\(x\\), i.e.,

\\[\bigcup_{o \in x} f_1(o)\\]

However, for formal concept analysis we use a different lifting, which is based on the _intersection_ of the sets.

Accordingly, define the left derivation operator \\(f: 2^X \rightarrow 2^Y\\) by

\\[f(x) = \bigcap_{o \in x} f_1(o)\\]

which is equivalent to

> let \\(f(x)\\) be the attributes which apply to every object in \\(x\\).

The standard way is to take the union of \\(f_1(o)\\) as \\(o\\) ranges over \\(x\\), i.e.,

\\[\bigcup_{o \in x} f_1(o)\\]

However, for formal concept analysis we use a different lifting, which is based on the _intersection_ of the sets.

Accordingly, define the left derivation operator \\(f: 2^X \rightarrow 2^Y\\) by

\\[f(x) = \bigcap_{o \in x} f_1(o)\\]

which is equivalent to

> let \\(f(x)\\) be the attributes which apply to every object in \\(x\\).