representation and replacement

Okay, suppose you have two objects, where one object A represents the other
object B, and you can always obtain one object from the other.

I would like to write A = B (to do replacements), but technically, they are
not of the same type, so it doesn't seem like you can really say they are
equal unless you accept the abuse of notation.

I though of using the logical equivalence symbol, but these are objects and
not truth statements.

What should I do?


.

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