On the Recollements of Functor Categories

This paper is devoted to the study of recollements of functor categories in different levels. In the first part of the paper, we start with a small category (mathcal {S}) and a maximal object s of (mathcal {S}) and construct a recollement of (text {Mod-}mathcal {S}) in terms of (text {Mod-End}_{mathcal {S}}(s)) and (text {Mod-}(mathcal {S}setminus {s})) in four different levels. In case (mathcal {S}) is a finite directed category, by iterating this argument, we get chains of recollements having some interesting applications. In the second part, we start with a recollement of rings and construct a recollement of their path rings, with respect to a finite quiver. Third part of the paper presents some applications, including recollements of triangular matrix rings, an example of a recollement in Gorenstein derived level and recollements of derived categories of N-complexes.