A Grothendieck category is n-coherent exactly when its FP_n objects are closed under kernels of epimorphisms, equivalently when FP_n equals FP_infinity.
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Locally type $\text{FP}_n$ and $n$-coherent categories
A Grothendieck category is n-coherent exactly when its FP_n objects are closed under kernels of epimorphisms, equivalently when FP_n equals FP_infinity.