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I'm reading Lang's section on field theory and he stresses that, unlike typical "universal" constructions which are determined up to unique isomorphism, algebraic closures (and by extension, their Galois groups) are determined only up to automorphism (conjugation). It seems to me that there ought to be some interpretation of this in terms of bicategories (weak 2-categories). This intuition is supported by the fact that 2-cells are given by conjugation when we give Grp the structure of a 2-category (view groups as 1-object categories, get 2-cells via natural transformations). Is there any such interpretation?

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