Spectra and Support Theory for Wide Subcategories in $n$-Abelian Categories

Abstract

We develop a support theory for wide subcategories of essentially small Krull--Schmidt \(n\)-abelian categories. We construct spectra associated with families of wide subcategories and establish the corresponding support and radical theories. In particular, we characterize prime wide subcategories as the completely meet-irreducible elements of the lattice of wide subcategories and prove that every wide subcategory is recovered from the prime wide subcategories containing it. We further show that any classifying support datum is recovered, together with its object supports, from the canonical prime spectrum. Finally, we provide a \(2\)-abelian example admitting no classifying support datum.