The question of how difucult it is to find an isomorphism between two structures is a key area of computable model theory and has lead notions like computably categorical structurs and the degree of categoricity of a struture. In this talk we study this question a class of problems in the Weihrauch degrees.
We define cat(M) for some countable strucuture M to be the problem who's instances are pairs of isomorphic copies (A,B) of M and who's solutions are isomorphisms between A and B.As one might expect the degree of categoricity of a structure has a relationship with it's Weihrauch degree, with id being the degree of uniformly computably categorical structures, but uniformity is important here as it turns out there are computably categorical structures that are stricly above id in the Weihrauch degrees. We also study the general cat problem who's instances are pairs of isomorphic stuctures without restricting to one particular base structure M. This problem ends up being equivalent ot choice oh Baire space.