Geodesic
Adjunction in 2-categories
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 75 (2020) no. 5, pp. 883-927 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{RM_2020_75_5_a2,
     author = {D. V. Kaledin},
     title = {Adjunction in 2-categories},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {883--927},
     year = {2020},
     volume = {75},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2020_75_5_a2/}
}
TY  - JOUR
AU  - D. V. Kaledin
TI  - Adjunction in 2-categories
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2020
SP  - 883
EP  - 927
VL  - 75
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/RM_2020_75_5_a2/
LA  - en
ID  - RM_2020_75_5_a2
ER  - 
%0 Journal Article
%A D. V. Kaledin
%T Adjunction in 2-categories
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2020
%P 883-927
%V 75
%N 5
%U http://geodesic.mathdoc.fr/item/RM_2020_75_5_a2/
%G en
%F RM_2020_75_5_a2
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/

[1] R. Anno, T. Logvinenko, “Spherical DG-functors”, J. Eur. Math. Soc. (JEMS), 19:9 (2017), 2577–2656 | DOI | MR | Zbl

[2] R. Anno, T. Logvinenko, $\mathbb{P}^n$-functors, 2019, 80 pp., arXiv: 1905.05740

[3] J. Bénabou, “Introduction to bicategories”, Reports of the Midwest category seminar, Lecture Notes in Math., 47, Springer, Berlin, 1967, 1–77 | DOI | MR | Zbl

[4] A. I. Bondal, M. van den Bergh, “Generators and representability of functors in commutative and noncommutative geometry”, Mosc. Math. J., 3:1 (2003), 1–36 | DOI | MR | Zbl

[5] A. K. Bousfield, “Constructions of factorization systems in categories”, J. Pure Appl. Algebra, 9:2 (1976/77), 207–220 | DOI | MR | Zbl

[6] P. Deligne, J. S. Milne, “Tannakian categories”, Hodge cycles, motives, and Shimura varieties, Lecture Notes in Math., 900, Springer-Verlag, Berlin–New York, 1982, 101–228 | MR | Zbl

[7] A. Grothendieck, “Catégories fibrée et descente”, Revêtements étales et groupe fondamental (SGA 1), Séminaire de géométrie algébrique du Bois Marie 1960–61, Doc. Math. (Paris), 3, 2nd ed., Soc. Math. France, Paris, 2003, Exp. VI, 119–151 | MR | Zbl

[8] V. Hinich, “Homological algebra of homotopy algebras”, Comm. Algebra, 25:10 (1997), 3291–3323 | DOI | MR | Zbl

[9] D. Kaledin, “Trace theories and localization”, Stacks and categories in geometry, topology, and algebra, Contemp. Math., 643, Amer. Math. Soc., Providence, RI, 2015, 227–262 | DOI | MR | Zbl

[10] D. B. Kaledin, “Witt vectors, commutative and non-commutative”, Russian Math. Surveys, 73:1 (2018), 1–30 | DOI | DOI | MR | Zbl

[11] D. Kaledin, Trace theories, Bökstedt periodicity and Bott periodicity, 2020, 210 pp., arXiv: 2004.04279

[12] B. Keller, “On differential graded categories”, International congress of mathematicians, v. II, Eur. Math. Soc., Zürich, 2006, 151–190 | MR | Zbl

[13] S. Mac Lane, Categories for the working mathematician, Grad. Texts in Math., 5, 2nd ed., Springer-Verlag, New York, 1998, xii+314 pp. | MR | Zbl

[14] D. Orlov, “Smooth and proper noncommutative schemes and gluing of DG categories”, Adv. Math., 302 (2016), 59–105 | DOI | MR | Zbl

[15] G. Segal, “Categories and cohomology theories”, Topology, 13:3 (1974), 293–312 | DOI | MR | Zbl