Highest weight categories arising from Khovanov's diagram algebra II: Koszulity

TL;DR

This paper develops the theory of projective functors in generalized Khovanov diagram algebras and proves their quasi-hereditary covers are Koszul, advancing understanding of algebraic structures related to categorification.

Contribution

It introduces the theory of projective functors for generalized Khovanov algebras and proves their covers are Koszul, providing new insights into their algebraic properties.

Findings

Proved quasi-hereditary covers of generalized Khovanov algebras are Koszul.

Developed the theory of projective functors in this algebraic setting.

Enhanced understanding of the structure of Khovanov diagram algebras.

Abstract

This is the second of a series of four articles studying various generalisations of Khovanov's diagram algebra. In this article we develop the general theory of Khovanov's diagrammatically defined "projective functors" in our setting. As an application, we give a direct proof of the fact that the quasi-hereditary covers of generalised Khovanov algebras are Koszul.