While proving no-ghost theorem ($4.4$ Polchinski) the term cohomology of $Q_B$ is used quite a lot of time. From what I understand this has to be a set since "cohomology of $Q_B$" is isomorphic to Hilbert space of OCQ or light cone quantization. Above $(4.2.18)$ following statement is made about the meaning of cohomology:
There is a natural construction for a nilpotent operator, and is known as cohomology of $Q_B$
By above statement isomorphism to Hilbert space loses its meaning. After reading Wikipedia I understand that cohomology is a collection of quotient sets and to define them you need chains (sequence of maps of sets satisfying certain conditions). I can't fit these ideas together to give meaning to cohomology of $Q_B$.