Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  establish that the local state monad introduced by Plotkin and Por is a monad with graded arities in the category (Inj,Set). From this,  deduce that the local state monad is associ- ated to a graded Lawvere theory מ� which is presented by generators and relations, depicted in the graphical language of string diagrams.
['Paul-André Melliès']
I am writing a research paper on a idea Local States in String Diagrams
[{"from": "human", "value": "I am writing a research paper on a idea Local States in String Diagrams"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  establish that the local state monad introduced by Plotkin and Por is a monad with graded arities in the category (Inj,Set). From this,  deduce that the local state monad is associ- ated to a graded Lawvere theory \u05de\ufffd which is presented by generators and relations, depicted in the graphical language of string diagrams."}]