Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies several applications of the notion of a presentation of a functor by operations and equations.  show that the technically straightforward generalisation of this notion from the one-sorted to the many-sorted case has several interesting consequences. First, it can be applied to give equational logic for the binding algebras modelling abstract syntax. Second, it provides a categorical approach to algebraic semantics of first-order logic. Third, this notion links the uniform treatment of logics for coalgebras of an arbitrary type T with concrete syntax and proof systems. Analysing the many-sorted case is essential for modular completeness proofs of coalgebraic logics.
['Alexander Kurz', 'Daniela Petrişan']
I am writing a research paper on a idea Presenting functors on many-sorted varieties and applications
[{"from": "human", "value": "I am writing a research paper on a idea Presenting functors on many-sorted varieties and applications"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies several applications of the notion of a presentation of a functor by operations and equations.  show that the technically straightforward generalisation of this notion from the one-sorted to the many-sorted case has several interesting consequences. First, it can be applied to give equational logic for the binding algebras modelling abstract syntax. Second, it provides a categorical approach to algebraic semantics of first-order logic. Third, this notion links the uniform treatment of logics for coalgebras of an arbitrary type T with concrete syntax and proof systems. Analysing the many-sorted case is essential for modular completeness proofs of coalgebraic logics."}]