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Uspekhi Mat. Nauk, 2020, Volume 75, Issue 5(455), Pages 101–152 (Mi umn9963)  

Adjunction in 2-categories

D. V. Kaledinab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b National Research University Higher School of Economics

Abstract: 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.

Funding Agency Grant Number
Russian Science Foundation 18-11-00141
This work was supported by the Russian Science Foundation under grant no. 18-11-00141. No funding came from any other source.


DOI: https://doi.org/10.4213/rm9963

Full text: PDF file (851 kB)
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English version:
Russian Mathematical Surveys, 2020, 75:5, 883–927

Bibliographic databases:

UDC: 512.667
MSC: 18N10
Received: 25.05.2020

Citation: D. V. Kaledin, “Adjunction in 2-categories”, Uspekhi Mat. Nauk, 75:5(455) (2020), 101–152; Russian Math. Surveys, 75:5 (2020), 883–927

Citation in format AMSBIB
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