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

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The discussion centers on the representation of the function g:A²→B², defined as g(x,y) = (f(x), f(y)), in relation to the function f:A→B. The notation gxg: A×A → B×B is confirmed as a well-understood representation for this type of function mapping. Participants agree that this notation effectively conveys the relationship between the input and output sets. The conversation highlights the importance of clear mathematical notation in function representation.

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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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