Let $X$ be a topological space and $\mathscr{F}$ a sheaf on $X$. In the paper Tropical cycle classes for non-archimedean spaces and weight decomposition of de Rham cohomology sheaves by Yifeng Liu, the notation $\underline{H}^p(X, \mathscr{F})$ is used. (More generally, $\mathscr{F}$ could be an object of the derived category of sheaves on $X$, e.g. some complex of sheaves.) For example we have the expression $H^0(X, \underline{H}^p(X, i_{Z!} i_Z^! \mathscr{K}_X^p))$ appearing right before Lemma 2.4 or $H^0(U, \underline{H}^p(U, i_{Z!}i_Z^! \mathscr{D}_U^{p,\bullet}))$ in the proof of Theorem 3.9.

It seems to be some kind of sheaf, but I cannot find its definition anywhere. Is it the sheaf associated to the presheaf $U \mapsto H^p(U, \mathscr{F})$? Where can I read some basic properties about this construction? I searched in the Stacks Project, in Hartshorne, Lei Fu's book on etale cohomology, Gelfand-Manin's homological algebra, but I couldn't find it.