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 Incoming links: Weakly initial set

Solution-set condition Created 2026-10-06 Updated 2026-10-07

For

U : C \to D

(D ↓ U)

. Equivalently, there is a set of arrows

d_{i} : D \to U C_{i}

through which every

d : D \to U C

factors as

U (h) d_{i}

. The dual right-adjoint condition asks for weakly terminal solution sets in

(U ↓ D)

A weakly terminal set is a set of objects

(W_{i})

of a category such that every object admits at least one morphism into some

W_{i}

. It is the dual of a weakly initial set.