= Limits in a comma category of a limit-preserving functor
If $G:\mathcal C\to\mathcal D$ preserves small <categorical limits>, the projection $(X\downarrow G)\to\mathcal C$ creates the small <categorical limits> available in $\mathcal C$. A <categorical cone> of arrows $X\to GA_j$ induces a unique arrow $X\to G(\lim A_j)$ by preservation; this equips the underlying <categorical limit> with its <comma category> structure. The <universal property> proves that every <categorical cone> factorization preserves that structure.
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