= Solution
For a diagram $D:\mathcal J\to\mathcal C$, a <limit-preserving functor> carries every limiting <cone over a diagram> to a limiting <categorical cone>. A <limit-reflecting functor> has the converse property: a <categorical cone> is limiting whenever its image is limiting. A <limit-creating functor> uniquely lifts every specified limiting <categorical cone> over the image diagram to a <categorical cone> over $D$, and the lift is limiting. These definitions concern diagrams of the stipulated shape; creation includes the lifting requirement, not merely reflection.
Let $(L,(p_j))$ be a <categorical limit> of $D$. The map
$$
\mathcal C(A,L)\longrightarrow\lim_j\mathcal C(A,Dj),\qquad h\longmapsto(p_jh)_j
$$
is a <bijection>: the right side consists exactly of compatible families of arrows from $A$, and the <categorical limit>'s <universal property> gives their unique factorization through $L$. The <bijection> is induced by the <categorical limit> projections, so it proves that <covariant representables preserve limits>, including the empty diagram and its <terminal object>.
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