Generalizations of the relationship between quasi-hereditary algebras and directed bocses

Koenig, K"ulshammer and Ovsienko showed that Morita equivalence classes of quasi-hereditary algebras are in one-to-one correspondence with equivalence classes of the module categories over directed bocses. In this article, we extend this result to $\mathrm{\Delta }$-filtered algebras and $\bar{\mathrm{\Delta }}$-filtered algebras.