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.


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