Non-compactly generated categories
The paper answers the following question raised by \textit{J. H. Palmieri} in affirmative: Is there a triangulated category which is not compactly generated? The topological terms ``triangulated'' and ``compactly generated'' are used here in categorical terms, e.g., an object \(c\) of a category \({\mathcal T}\) is called compact if any map from it to any coproduct of objects in \({\mathcal T}\) factors through a finite coproduct. The counterexample produced by the author has many interesting features. He uses in his construction the nice category of \(H\)-local objects where \(H\) is a homology theory. The category of \(H\)-local objects has tensor products which have an adjoint. The counterexample is obtained from the derived category of a commutative local Noetherian integral domain \(R\) of dimension greater than one by localizing \(D(R)\) with respect to the homology theory given by smashing with \(k\oplus K\) where \(k\) is the residue field and \(K\) is the quotient field.
scientific article; zbMATH DE number 1307789