2017/02/23 by Dean, Samuel
#18E05 #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1702.07184
In this expository article, we will give an efficient functorial proof of the equivalence of various characterisations of purity in a finitely accessible additive category \mathcal C. The complications of the proofs for specific choices of \mathcal C are contained in the description of fp-injective and injective objects in (fp\mathcal C,Ab), the category of additive functors \mathcal C\toAb. For example, the equivalence of many characterisations of purity in a module category \mathcal A-Mod is a simple corollary of what we will prove here, since we know which objects are fp-injective, and which objects are injective, in (\mathcal A-mod,Ab).