Relative theories(=closed subfunctors) are considered in exact, triangulated and extriangulated categories by Dräxler-Reiten-Smalø-Solberg-Keller, Beligiannis and HerschendLiu-Nakaoka, respectively. We give a construction method of closed subfunctors from given half exact functors which contains existing constructions. Moreover, if an extriangulated category has enough projective objects, then every closed subfunctor is obtained by this construction.

We give a simultaneous generalization of exact categories and triangulated categories, which is suitable for considering cotorsion pairs, and which we call extriangulated categories.… Expand

It is proved that for a given skeletally small additive category, the poset of exact structures on it is isomorphic to thePoset of Serre subcategories of some abelian category.Expand

In a series of papers additive subbifunctors F of the bifunctor ExtΛ( , ) are studied in order to establish a relative homology theory for an artin algebra Λ. On the other hand, one may consider the… Expand

An additive category with direct limits is said to be locally nitely presented provided that the full subcategory of nitely presented objects is skeletally small and every object is a direct limit of… Expand

The general theory of locally coherent Grothendieck categories is presented. To each locally coherent Grothendieck category C a topological space, the Ziegler spectrum of C, is associated. It is… Expand