Pure Extending Objects

Abstract

In this paper we introduce two new concepts, namely, pure extending objects and $\mathcal{K}$-nonsingular objects and then, we prove that any pair of subisomorphic $\mathcal{K}$-nonsingular objects in a finitely accessible additive category with kernels $\mathcal{A}$ are isomorphic to each other if and only if for any object $Y$ and any pure extending $\mathcal{K}$-nonsingular object $X$, if $X$ and $Y$ are subisomorphic to each other then $X\cong Y$.

Keywords

• Finitely accessible category
• Pure essential monomorphism
• Nonsinguler object

References

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