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I moved the characterization of pointwise kan extensions as those preserved by representable functors to the top (of the section on pointwise kan extensions) and made it the definition (since there was no unified definition before). This is for aesthetic reasons. Since being pointwise is a property, I like that this property has a definition independent of the computational model we’re using.
Are there size issues that I might be glossing over?
Well, “representable functors” only exist if your category is locally small, or if you use a higher universe in which for them to take values, if that’s what you’re thinking of. I don’t think we need to dwell on anything like that at Kan extension though.
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