Representing a Function g:A2->B2 Using f:A->B: Quick Notation Question

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The function g:A2->B2 can be represented as g(x,y) = (f(x), f(y)), indicating that it takes a pair of inputs from A and outputs a pair in B. The notation gxg: AxA --> BxB is commonly understood to describe this relationship. This representation aligns with standard practices in function notation for Cartesian products. The discussion confirms that this notation is intuitive, even if not frequently seen in writing. Overall, the representation of g using f is straightforward and follows established conventions.
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Given the function f:A->B, what would be the usual way of representing the function g:A2->B2 where g(x,y) = (f(x),f(y))?
 
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usually gxg: AxA --> BxB would be well understood.
 
tahnks, I thought it was prolly something like that, though I hadn't seen it writtn before.
 

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