Henn, Hans-Werner; Lannes, Jean; Schwartz, Lionel The categories of unstable modules and unstable algebras over the Steenrod algebra modulo nilpotent objects. (English) Zbl 0805.55011 Am. J. Math. 115, No. 5, 1053-1106 (1993). 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. Reviewer: J.Hodgson (Philadelphia) Cited in 8 ReviewsCited in 45 Documents MathOverflow Questions: About the abelian category of endofunctors of \(\mathsf{Vect}\) MSC: 55S10 Steenrod algebra 55U99 Applied homological algebra and category theory in algebraic topology 18E20 Categorical embedding theorems Keywords:analytic functor; elementary abelian \(p\)-group; category of unstable modules over the mod \(p\) Steenrod algebra × Cite Format Result Cite Review PDF Full Text: DOI