Abstract
The paper is devoted to a kind of “very non-abelian” spectral categories. Under strong conditions on a category $\mathcal X$, we prove, among other things, that, for a given faithful localization $\mathcal C \to \mathcal X$, we have canonical equivalences Spec$(\mathcal{C})\sim\mathcal{X}\sim$(category of injective objects in $\mathcal{C})$, and that $\mathcal{C}$ has natural injective envelopes.
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