Solution-set condition
= Solution-set condition
For $U:\mathcal C\to\mathcal D$, the left-adjoint solution-set condition requires a <weakly initial set> in every $(D\downarrow U)$. Equivalently, there is a <set> of arrows $d_i:D\to UC_i$ through which every $d:D\to UC$ factors as $U(h)d_i$. The dual right-adjoint condition asks for weakly terminal solution sets in $(U\downarrow D)$.