… of flatness and absolute purrty in functor categories (Proposition 1, Oberst and Rohrl [7],
Lenzing [4]) p rovide new characterizations of flatness and absolute purity in module categories. …

… When one deals with functor categories in representation theory or the theory of triangulated
categories, one, however, often encounters a non-noetherian categories. Treating the …

… First, the absolute theory in a triangulated category, ie, if we … the pure Brown categories as
the pure hereditary ones, and … the fullness of the projectivization functor and the conditions …

… derived category of all modules. We answer the natural question whether this functor defines
an … So, in this particular respect, absolute derived categories are better behaved than …

… Absolutely pure R-modules are investigated in [16] and []8]. In the present article we give the
conditions for a sub M-set to be pure and exanine absolutely pure … flat if the functor OMA pre…

… category of right unitary /^-modules over the associative ring JR with 1, we shall introduce and
examine the concept of weak g-purity… Since this functor is left exact, the first derived functor …

… categories, the corresponding pure-injective objects are quite different. Section 2 looks deeper
into the purity-related notions in the category \(… by the three functors associated to an open …

… , and derived functors by relative derived functors. A classical example of this is pure homological
algebra where the projective modules are replaced by the so-called pure projective …

… ideas and methods from model theory and functor category theory. Purity and associated
notions are central, localisation … Pure global dimension Absolutely pure and flat modules 2.3.1 …

… Adjoint Functor Theorem is due to the pure formal properties of the concepts involved … of
V-functor categories, which we do in the next chapter, where we state the (absolute) theorems of …