Flat Objects and Cotorsion Pairs in Functor Categories

Specialeforsvar ved Benjamin Pedersen

Titel: Flat Objects and Cotorsion Pairs in Functor Categories

Abstract: This thesis is concerned with the abelian category Fun(I,M) of functors from a small category I to an abelian category M. Under certain assumptions, the flat objects in Fun(I,M) are characterized as a certain class _(FlatM) \ Fun(I, FlatM) where flat objects are defined to be direct limits of projective objects. This is a direct generalization of a characterization of the flat objects in Rep(Q,R-Mod) by Enochs, Oyonarte, and Torrecillas from 2004. Under different sets of assumptions, it is shown that a cotorsion pair (A, B) in M induce two explicitly described cotorsion pairs (_(A), Fun(I, B)) and (Fun(I,A), (B)) in Fun(I,M). This is a direct generalization of a construction of two cotorsion pairs in Rep(Q,M) by Holm and Jørgensen from 2016.

Vejleder: Henrik G. Holm
Censor:    Niels Lauritzen, Aarhus Universitet