𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Brown representability and flat covers

✍ Scribed by Henning Krause

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
66 KB
Volume
157
Category
Article
ISSN
0022-4049

No coin nor oath required. For personal study only.

✦ Synopsis

We exhibit a surprising connection between the following two concepts: Brown representability which arises in stable homotopy theory, and at covers which arise in module theory. It is shown that Brown representability holds for a compactly generated triangulated category if and only if for every additive functor from the category of compact objects into the category of abelian groups a at cover can be constructed in a canonical way. The proof also shows that Brown representability for objects and morphisms is a consequence of Brown representability for objects and isomorphisms.

πŸ“œ SIMILAR VOLUMES

Flat covers and factorizations
Flat covers and factorizations
✍ J. RosickΓ½ πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 97 KB

The flat cover conjecture, saying that every module has a flat (pre)cover, has been recently proved by Bican, El Bashir, and Enochs. We relate flat precovers (and cotorsion preenvelopes) to weak factorizations and prove that flat monomorphisms form a left part of a weak factorization system.

Covers and Envelopes in Grothendieck Cat
Covers and Envelopes in Grothendieck Categories: Flat Covers of Complexes with Applications
✍ S.Tempest Aldrich; Edgar E Enochs; J.R Garcı́a Rozas; Luis Oyonarte πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 136 KB

In the general setting of Grothendieck categories with enough projectives, we prove theorems that make possible to restrict the study of the problem of the existence of -covers and envelopes to the study of some properties of the class . We then prove the existence of flat covers and cotorsion envel

Derived Functors of Hom Relative to Flat
Derived Functors of Hom Relative to Flat Covers
✍ Stephen T. Aldrich; Edgar E. Enochs; Juan A. Lopez Ramos πŸ“‚ Article πŸ“… 2002 πŸ› John Wiley and Sons 🌐 English βš– 168 KB