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\$$.