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Mathematics, Category Theory, Quantum Algebra
Abstract:
We give a definition of a coherent adjunction in a 4-category consisting of a finite list of k-morphisms for k≤4, plus equations beetween 4-morphisms. We prove that the restriction map from the space of coherent adjunctions in a 4-category to the space of 1-morphisms which admit an adjoint is a trivial fibration. We prove that other restriction maps related to fixing parts of the data of an adjunction are also trivial fibrations. We give a conjectural description of a coherent adjunction in an n-category.
