… tilting object in a cocomplete abelian category A induces a tilting theorem between A and the
category … Y, then there is a tilting object V in a cocomplete abelian category A such that R = …

… We show that for the abelian category A to have a tilting object it is necessary that the
Grothendieck group is free of finite rank and that A has almost split sequences. In the last section …

… We also show that an Ext-finite hereditary abelian R-category H with tilting object is … abelian
category. Most of the results for Ext-finite hereditary abelian categories with tilting object over …

… to tilting theory will be exhibited. In a sense we shall prove that almost abelian categories and
tilting are two … , ie each object isomorphic to some object in A also belongs to A. Then A is …

… tilting theory gives a way to construct abelian categories from some triangulated categories.
… We write an object D in the form \(\Omega B\) if it admits an \({\mathbb {E}}\)-triangle where \(…

… -)tilting objects in arbitrary Abelian categories and show that tilting objects are Ext1-universal
(see Proposition 5.7). We show that our general concept of (quasi-)tilting object coincides …

… These categories will be the main object of this article. … To any almost abelian category
we shall associate (§3) a pair of abelian full subcategories Ao and A. If A is a PI-category, then …

… them as pairs (A, B) of classes of objects of an abelian category C such that Exti … nX-tilting
theory developed in the abelian category Mod(Pop) is strongly related with the small n-tilting …

… In Section 6, we introduce the notion of tilting and cotilting objects in abelian categories,
which is an extension of the definition given by Angeleri-Coehlo [Citation3] for the setting of the …

… generator is equivalent to a module category [23]. A tilting object in a abelian category is a
natural … Moreover, any abelian category with a tilting object admits arbitrary coproducts [12]. It …