Applications of the defect of a finitely presented functor

JOURNAL OF ALGEBRA

卷:465

Article

Russell, Jeremy¹ 

[1] Coll New Jersey, Ewing, NJ 08628 USA

关键词: Finitely presented functors;    Coherent functors;    Categorical algebra;    Almost split sequences;    Injective stabilization;    Derived functors;   

DOI  :  10.1016/j.jalgebra.2016.07.016

来源: Elsevier

【 摘 要 】

For an abelian category A, the defect sequence 0 -> F-0 -> F -> (w(F), _) -> F-1 -> 0 of a finitely presented functor is used to establish the CoYoneda Lemma. An application of this result is the fp-dual formula which states that for any covariant finitely presented functor F, F* congruent to (_, w(F)). The defect sequence is shown to be isomorphic to both the double dual sequence 0 -> Ext(1) (TrF, Hom) -> F -> F** -> Ext(2) (TrF, Hom) -> 0 and the injective stabilization sequence 0 -> (F) over bar -> F -> (RF)-F-0 -> (F) over tilde -> 0 establishing the fp-injective stabilization formula (F) over bar congruent to Ext(1) (TrF, Hom) for any finitely presented functor F. The injectives of fp(Mod(R),Ab) are used to compute the left derived functors L-k(_)*. These functors are shown to detect certain short exact sequences in Mod(R). (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free