Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  prove that every finitary polynomial endofunctor of a category $C$ has a final coalgebra if $C$ is locally Cartesian closed, has finite disjoint coproducts and a natural number object. More generally,  prove that the category of coalgebras for such an endofunctor has all finite limits.
['Luigi Santocanale']
I am writing a research paper on a idea Logical Construction of Final Coalgebras
[{"from": "human", "value": "I am writing a research paper on a idea Logical Construction of Final Coalgebras"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  prove that every finitary polynomial endofunctor of a category $C$ has a final coalgebra if $C$ is locally Cartesian closed, has finite disjoint coproducts and a natural number object. More generally,  prove that the category of coalgebras for such an endofunctor has all finite limits."}]