Brown Representability Test Problems in Locally Grothendieck Categories

Abstract

Open questions concerning Brown representability have recently led Rosicky and Muro to formulate two test problems for Grothendieck categories. We prove that these test problems have a negative solution in the locally Grothendieck category C = boolean OR(kappa }=aleph 0) Mod-K-kappa where K is a field.

Keywords

• Brown representability
• Grothendieck category
• kappa-purity