Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: For any category of interest ℂ  define a general category of groups with operations \(\mathbb{C_G}, \mathbb{C}\hookrightarrow\mathbb{C_G}\), and a universal strict general actor USGA(A) of an object A in ℂ, which is an object of \(\mathbb{C_G}\). The notion of actor is equivalent to the one of split extension classifier defined for an object in more general settings of semi-abelian categories. It is proved that there exists an actor of A in ℂ if and only if the semidirect product \({\text{USGA}}(A)\ltimes A\) is an object of ℂ and if it is the case, then USGA(A) is an actor of A.  give a construction of a universal strict general actor for any A ∈ ℂ, which helps to detect more properties of this object. The cases of groups, Lie, Leibniz, associative, commutative associative, alternative algebras, crossed and precrossed modules are considered. The examples of algebras are given, for which always exist actors.
['J. M. Casas', 'Tamar Datuashvili', 'M. Ladra']
I am writing a research paper on a idea Universal Strict General Actors and Actors in Categories of Interest
[{"from": "human", "value": "I am writing a research paper on a idea Universal Strict General Actors and Actors in Categories of Interest"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: For any category of interest \u2102  define a general category of groups with operations \\(\\mathbb{C_G}, \\mathbb{C}\\hookrightarrow\\mathbb{C_G}\\), and a universal strict general actor USGA(A) of an object A in \u2102, which is an object of \\(\\mathbb{C_G}\\). The notion of actor is equivalent to the one of split extension classifier defined for an object in more general settings of semi-abelian categories. It is proved that there exists an actor of A in \u2102 if and only if the semidirect product \\({\\text{USGA}}(A)\\ltimes A\\) is an object of \u2102 and if it is the case, then USGA(A) is an actor of A.  give a construction of a universal strict general actor for any A \u2208 \u2102, which helps to detect more properties of this object. The cases of groups, Lie, Leibniz, associative, commutative associative, alternative algebras, crossed and precrossed modules are considered. The examples of algebras are given, for which always exist actors."}]