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The collection of open sets of a topological space forms a Heyting algebra,which leads to the idea of a Heyting algebra as a generalized topologicalspace. In fact, a sober topological space may be reconstructed from its localeof open sets. This has given rise to a good theory of presheaves and sheavesover locales. At the same time, several ring like properties of Heytingalgebras have also been studied. The purpose of this paper is to study anon-abelian homological theory for modules over Heyting algebras.

Homological Algebra of Heyting modules