  We give a category-theoretic construction of simple and NSOP$_1$-like
independence relations in locally finitely presentable categories, and in the
more general locally finitely multipresentable categories. We do so by
identifying properties of a class of monomorphisms $\mathcal{M}$ such that the
pullback squares consisting of morphisms in $\mathcal{M}$ form the desired
independence relation. This generalizes the category-theoretic construction of
stable independence relations using effective unions or cellular squares by M.
Lieberman, S. Vasey and the second author to the unstable setting.
