Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show that for a commutative quantale V every functor from Set to V-cat has an enriched left-Kan extension. As a consequence, coalgebras over Set are subsumed by coalgebras over V-cat. Moreover, one can build functors on V-cat by equipping Set-functors with a metric.
['Adriana Balan', 'Alexander Kurz', 'Jiri Velebil']
I am writing a research paper on a idea Extensions of Functors From Set to V-cat
[{"from": "human", "value": "I am writing a research paper on a idea Extensions of Functors From Set to V-cat"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show that for a commutative quantale V every functor from Set to V-cat has an enriched left-Kan extension. As a consequence, coalgebras over Set are subsumed by coalgebras over V-cat. Moreover, one can build functors on V-cat by equipping Set-functors with a metric."}]