2022/07/07 by Manuel Mora y Araujo, Araújo, Manuel
Mathematics · #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2207.02935
openalex publication_date 2022/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.