Limits in a reflective subcategory
= Limits in a reflective subcategory
If a <full subcategory> is reflective in a <complete category>, it is complete. For an ambient limit $L$ of a diagram of reflected objects, the reflection unit $L\to JKL$ is invertible by the <hom-set> characterization of reflected objects. Thus $KL$ is an internal <categorical limit>. If the subcategory is replete, $L$ itself belongs to it. The <reflector> need not preserve arbitrary limits.