Abstract
In this note, we investigate some finiteness properties of the category 𝓤 of unstable modules over the Steenrod algebra. We show a finiteness property for the injective resolution of finitely generated unstable modules: we show that such a module has an injective resolution, such that each term is a finite direct sum of indecomposable injective unstable modules. We also show a stabilization result under Frobenius twist for Ext𝓤-groups.
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