In di-exact categories, modularity and distributivity of the lattice of normal subobjects characterize homological properties, and concrete examples separate homological self-duality, DPN, and di-exactness.
Birkhoff, Lattice theory, Amer
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Di-Exact Categories and Lattices of Normal Subobjects
In di-exact categories, modularity and distributivity of the lattice of normal subobjects characterize homological properties, and concrete examples separate homological self-duality, DPN, and di-exactness.