  We introduce three general compositionality criteria over operational
semantics and prove that, when all three are satisfied together, they guarantee
weak bisimulation being a congruence. Our work is founded upon Turi and
Plotkin's mathematical operational semantics and the coalgebraic approach to
weak bisimulation by Brengos. We demonstrate each criterion with various
examples of success and failure and establish a formal connection with the
simply WB cool rule format of Bloom and van Glabbeek. In addition, we show that
the three criteria induce lax models in the sense of Bonchi et al.
