Is it possible to define (possibly derived) categories of constructible sheaves over sites more general than those of open subsets of topological spaces while still retaining essential features, like how if $\Lambda$ is a Noetherian ring then constructible sheaves of $\Lambda$-modules will span a thick subcategory of the abelian category of sheaves of $\Lambda$-modules ? Will such a generalisation of constructible sheaves involve defining stratifications of sites/sheaf topoi, and if so, how would we go about defining such notions of stratifications ?
In particular, I am interested in "direct" definitions of constructible étale, lisse-étale, and fppf sheaves over a given scheme/algebraic space/Artin stack $X$. Certain restrictions that I am willing to work under are that $X$ is (locally) of finite type over some base scheme $S$ that is affine, regular, Noetherian, of dimension $\leq 1$, and of characteristic $p \geq 0$, and that the ring of coefficient $\Lambda$ is a Gorenstein local ring of dimension $0$ and characteristic $\ell \not = p$.
