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- W4297658553 abstract "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 $(operatorname{fp}mathcal C,mathrm{Ab})$, the category of additive functors $mathcal Ctomathrm{Ab}$. For example, the equivalence of many characterisations of purity in a module category $mathcal Amathrm{-Mod}$ is a simple corollary of what we will prove here, since we know which objects are fp-injective, and which objects are injective, in $(mathcal Amathrm{-mod},mathrm{Ab})$." @default.
- W4297658553 created "2022-09-30" @default.
- W4297658553 creator A5045930247 @default.
- W4297658553 date "2017-02-23" @default.
- W4297658553 modified "2023-09-30" @default.
- W4297658553 title "Characterisations of purity in a locally finitely presented additive category: A short functorial proof" @default.
- W4297658553 doi "https://doi.org/10.48550/arxiv.1702.07184" @default.
- W4297658553 hasPublicationYear "2017" @default.
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