This would be intended to be like the adjoint to the inclusion of $Sub(X)$, the subsets of a set $X$ into $ \mathbf{Set}/X $, namely taking the image of a function--except "one level higher".
2026-03-28 08:09:50.1774685390
Is there a left adjoint to the inclusion of discrete (op)fibrations over $X$ into $\mathbf{Cat}/X$?
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The answer is yes, apparently. http://ncatlab.org/michaelshulman/show/comprehensive+factorization