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The categories of unstable modules and unstable algebras over the Steenrod algebra modulo nilpotent objects. (English) Zbl 0805.55011
Let $${\mathcal U}$$ (respectively $${\mathcal K}$$) denote the category of unstable $$A$$-modules (respectively unstable $$A$$-algebras) over the mod $$p$$ Steenrod algebra $$A$$. By “inverting” all morphisms in these categories with “nilpotent kernel and cokernel” one obtains quotient categories $${\mathcal U}/{\mathcal N}il$$ and $${\mathcal K}/{\mathcal N}il$$ which are objects of the study in this paper.
The main results identify these categories with certain explicit functor categories. In each case the category is the full subcategory of a functor category consisting of those objects that are the analytic functors.

MSC:
 55S10 Steenrod algebra 55U99 Applied homological algebra and category theory in algebraic topology 18E20 Categorical embedding theorems
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