= Additive category with truncated primary torsion
{title2=$\mathcal A_p$}
Fix a <prime number> $p$. Take the full <subcategory> of <finitely generated abelian groups> with no element of order $p^2$. It is closed under finite <direct sums> and <subgroups>. If $t_p(G)$ is the $p$-primary <torsion subgroup>, the map $G\to R(G)=G/(p\,t_p(G))$ is a <reflection> into this subcategory: every map to an allowed group kills $p\,t_p(G)$. Therefore ordinary <kernels in a category> and reflected <cokernels in a category> supply all finite <categorical limits> and <colimits>. No nonzero finitely generated group has zero reflection, so the <epimorphisms> are precisely surjections and are all <conormal epimorphisms>. Multiplication by $p^2$ on $\mathbb Z$ is a <monomorphism> but not a <normal monomorphism>: its cokernel here is $\mathbb Z/p\mathbb Z$, whose kernel is $p\mathbb Z$, not $p^2\mathbb Z$. Multiplication by $p$ is normal; composing it with itself gives this nonnormal monomorphism.
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