The Defect Functor of a Homomorphism and Direct Unions

Abstract

We will study commuting properties of the defect functor associate to a homomorphism in a finitely presented category. As an application, we characterize objects M such that commutes with direct unions (i.e. direct limits of monomorphisms), assuming that has a generator which is a direct sum of finitely presented projective objects.

Keywords

• Defect functor
• Coherent functor
• Direct limit
• Direct union
• Ext-functor