Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4583950 | Journal of Algebra | 2016 | 38 Pages |
Abstract
It is shown that the category of enriched functors [C,V] is Grothendieck whenever V is a closed symmetric monoidal Grothendieck category and C is a category enriched over V. Localizations in [C,V] associated to collections of objects of C are studied. Also, the category of chain complexes of generalized modules Ch(CR) is shown to be identified with the Grothendieck category of enriched functors [modR,Ch(ModR)] over a commutative ring R, where the category of finitely presented R-modules mod R is enriched over the closed symmetric monoidal Grothendieck category Ch(ModR) as complexes concentrated in zeroth degree. As an application, it is proved that Ch(CR) is a closed symmetric monoidal Grothendieck model category with explicit formulas for tensor product and internal Hom-objects. Furthermore, the class of unital algebraic almost stable homotopy categories generalizing unital algebraic stable homotopy categories of Hovey-Palmieri-Strickland [14] is introduced. It is shown that the derived category of generalized modules D(CR) over commutative rings is a unital algebraic almost stable homotopy category which is not an algebraic stable homotopy category.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Hassan Al Hwaeer, Grigory Garkusha,