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Sur les \({\mathcal U}\)-injectifs. (On \({\mathcal U}\)-injectives). (French) Zbl 0608.18006
The importance of injectives in the category of unstable modules over the mod p Steenrod algebra has recently been emphasized by the work of H. Miller [Ann. Math., II. Ser. 120, 39-87 (1984; Zbl 0552.55014)] and G. Carlsson [Topology 22, 83-103 (1983; Zbl 0504.55011)] relating to the Sullivan conjecture and its solution. In this paper, a study is made of certain types of these injectives. In particular the authors give conditions that imply that if J and K are such injectives, their tensor product \(K\otimes J\) is also injective. For \(p=2\) this result implies the principal result of J. F. Adams, J. Gunawardena and H. Miller [The Segal conjecture for \(({\mathbb{Z}}/p)^ R\), to appear].
{Remark: The first author in a joint paper with L. Schwartz (cited [19] in this note) has recently obtained more detailed results on these injectives.}
Reviewer: T.Porter

MSC:
18G05 Projectives and injectives (category-theoretic aspects)
55S10 Steenrod algebra
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References:
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