Abstract
$[\mathcal{A}^{o\mathrm{p}},\mathcal{L}\mathrm{at}]$ is a reflective and coreflective sub-2-category of Fun $[\mathcal{A}^{o\mathrm{p}} \mathcal{L}\mathrm{at}]$. Lax ends and pointwise lax extensions can be expressed by indexed limits using the above coreflector.
Citation
Symeon Bozapalides. "Some remarks on lax-presheafs." Illinois J. Math. 24 (4) 676 - 680, Winter 1980. https://doi.org/10.1215/ijm/1256047482
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