Coherence for adjunctions in a 4-category

Araújo, Manuel

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Coherence for adjunctions in a 4-category

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Araújo, Manuel
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.2207.02935
(Preprint)

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2207.02935.pdf
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Citation

Araújo, M. (submitted). Coherence for adjunctions in a 4-category.

Cite as: https://hdl.handle.net/21.11116/0000-0010-3B2B-D

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.