  Now let  E  be a full topos. If A = (A, R, …) is a structure, write A for (A, R, …).  Two structures A and B are said to be topos isomorphic, written A ≅t B, if, for some topos  E  defined over the category of sets, we have  E   ⊨ A ≅ B. In other words two structures are topos isomorphic if their canonical representatives are isomorphic in the internal language of some topos. It can then be shown that