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Componentwise injective models of functors to DGAs. (English) Zbl 0877.55004

The Sullivan theory of minimal models has been generalized by G. Triantafillou [Trans. Am. Math. Soc. 274, 509-532 (1982; Zbl 0516.55010)] to \(G\)-actions of a finite group on a simplicial set. The main tool in this equivariant theory is the notion of injective minimal models for a system of commutative DG-algebras associated to a connected and nilpotent \(G\)-simplicial set of \(\mathbb{Q}\)-finite type. In order to get rid of these two assumptions the author replaces the notion of finitely generated \(\mathbb{Q}\)-modules by those of a linearly compact \(\mathbb{Q}\)-module and establishes the starting point for proving the existence of injective minimal models for such system in a forthcoming paper.

MSC:

55P62 Rational homotopy theory
55N91 Equivariant homology and cohomology in algebraic topology
16W50 Graded rings and modules (associative rings and algebras)
18G05 Projectives and injectives (category-theoretic aspects)

Citations:

Zbl 0516.55010
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