Geodesic
Adjunction in 2-categories
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 75 (2020) no. 5, pp. 883-927

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The aim of the paper is to introduce an approach to the theory of 2-categories which is based on systematic use of the Grothendieck construction and the Segal Machine and to show how adjunction questions can be investigated by means of this approach and what its connections are with more traditional approaches. As an application, the derived Morita 2-category and the Fourier–Mukai 2-category over a Noetherian ring are constructed and the embedding of the latter in the former is demonstrated. Bibliography: 15 titles.
Keywords: adjoint functors, 2-categories. 
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     author = {D. V. Kaledin},
     title = {Adjunction in 2-categories},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {883--927},
     publisher = {mathdoc},
     volume = {75},
     number = {5},
     year = {2020},
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     url = {http://geodesic.mathdoc.fr/item/RM_2020_75_5_a2/}
}
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D. V. Kaledin. Adjunction in 2-categories. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 75 (2020) no. 5, pp. 883-927. http://geodesic.mathdoc.fr/item/RM_2020_75_5_a2/