Integrated vertex: case of

The zero curvature equation allows to give a unified description of integrated and unintegrated vertices.

We have:

(only modulo because ) This means that:

the operation of the substitution of intertwines with

Given the cocycle the following
expression:

gives a cohomology class of which is the sum of integrated and unintegrated vertex operator, and an
intermediate expression.

In other words, we expressed integrated and unintegrated operators as different components of the same cohomology class.