The subobject classifier of the category of quivers (already discussed in this series) is another good one to work through when learning about this stuff. You can use the characterization by sieves, but you can also think about it as subobjects of representables directly—remembering that it all works because of the isomorphisms
where is , , , or to figure out the corresponding aspect of . arXiv:math/0306394 walks through it all, though you might consider that to be a “spoiler” relative to figuring things out yourself.

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