Applications of the defect of a finitely presented functor

作者：Russell Jeremy^*

来源：Journal of Algebra, 2016, 465: 137-169.

DOI：10.1016/j.jalgebra.2016.07.016

• Finitely presented functors
• Coherent functors
• Categorical algebra
• Almost split sequences
• Injective stabilization
• Derived functors

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).

• 出版日期2016-11-1