Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterisations of purity in a locally finitely presented additive
  category: A short functorial proof   In this short note, we will give an efficient functorial proof of the
equivalence of various characterisations of purity in a locally finitely
presented additive category $C$. The complications of the proofs for specific
choices of $C$ (e.g. $C=A\text{-Mod}$ for a ring $A$) are contained in the
description of fp-injective and injective objects in $(\text{fp}C,\text{Ab})$.
For example, the equivalence of many characterisations of purity in a module
category $A\text{-Mod}$ is a simple corollary of what we will prove here, once
we know that $\text{Fpinj}(A\text{-mod},\text{Ab})$ and
$\text{Inj}(A\text{-mod},\text{Ab})$ look like (we do).

30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex