Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: By Boolean category  mean something which is to a Boolean algebra what a category is to a poset.  propose an axiomatic system for Boolean categories, which is different in several respects from the ones proposed recently In particular everything is done from the start in a *-autonomous category and not in a akly distributive one, which simplifies issues like the Mix rule. An important axiom, which is introduced later, is a "graphical" condition, which is closely related to denotational semantics and the Geometry of Interaction. Then  show that a previously constructed category of proof nets is the free "graphical" Boolean category in our sense. This validates our categorical axiomatization with respect to a real-life example. Another important aspect of this work is that  do not assume a-priori the existence of units in the *-autonomous categories  use. This has some retroactive interest for the semantics of linear logic, and is motivated by the properties of our example with respect to units.
['F. Lamarche', 'Lutz Strassburger']
I am writing a research paper on a idea Constructing free Boolean categories
[{"from": "human", "value": "I am writing a research paper on a idea Constructing free Boolean categories"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: By Boolean category  mean something which is to a Boolean algebra what a category is to a poset.  propose an axiomatic system for Boolean categories, which is different in several respects from the ones proposed recently In particular everything is done from the start in a *-autonomous category and not in a akly distributive one, which simplifies issues like the Mix rule. An important axiom, which is introduced later, is a \"graphical\" condition, which is closely related to denotational semantics and the Geometry of Interaction. Then  show that a previously constructed category of proof nets is the free \"graphical\" Boolean category in our sense. This validates our categorical axiomatization with respect to a real-life example. Another important aspect of this work is that  do not assume a-priori the existence of units in the *-autonomous categories  use. This has some retroactive interest for the semantics of linear logic, and is motivated by the properties of our example with respect to units."}]