Through the application of the Yoneda embedding in the context of the ∞- categories is obtained a classification of functors with their corresponding extended functors in the geometrical Langlands program. Also is obtained a functor formula that can be considered in the extending of functors to obtaining of generalized Verma modules. In this isomorphism formula are considered the Verma modules as classifying spaces of these functors.
| Published in |
Pure and Applied Mathematics Journal (Volume 3, Issue 6-2)
This article belongs to the Special Issue Integral Geometry Methods on Derived Categories in the Geometrical Langlands Program |
| DOI | 10.11648/j.pamj.s.2014030602.14 |
| Page(s) | 20-25 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2014. Published by Science Publishing Group |
Deformed Category, Extended Functor, Full and faithfull Functor, ∞- Category, Moduli Problem, Yoneda Embedding
| [1] | M. Kontsevich, Y. Soibelman, Deformations of algebras over operads and the Deligne conjecture, Conference Moshe Flato 1999, Vol 1 (Dijon), 255-307, Math. Phys. Stud., 21, Kluwer Acad. Publ., Dordrecht, 2000. |
| [2] | N. Yoneda (1954). “On the homology theory of modules”. J. Fac. Sci. Univ. Tokyo. Sect. I 7: 193–227. |
| [3] | S. Mac Lane (1998), Categories for the Workshop Mathematician, Graduate Texts in Mathematics 5 (2nd ed.), New York, NY: Springer-Verlag. |
| [4] | I. Verkelov, “Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories,” Pure and Applied Mathematics Journal. Vol. 3, No. 2, 2014, pp. 12-19. doi:10.11648/j.pamj.s.20140302.13 |
| [5] | V. Hinich, DG Deformations of homotopy algebras, Communications in Algebra, 32 (2004), 473-494. |
| [6] | K. Fukaya, Floer Homology and Mirror Symmetry I, Department of Mathematics, Faculty of Science, Kyoto University, Kitashirakawa, Kyoto, 606-8224, Japan. |
| [7] | A. Kapustin, M. Kreuser and K. G. Schlesinger, Homological mirror symmetry: New Developments and Perspectives, Springer. Berlin, Heidelberg, 2009. |
| [8] | F. Bulnes (2014) Framework of Penrose Transforms on DP-Modules to the Electromagnetic Carpet of the Space-Time from the Moduli Stacks Perspective. Journal of Applied Mathematics and Physics, 2, 150-162. doi:10.4236/jamp.2014.25019. |
| [9] | E. Sharp, “Derived Categories and Stacks in Physics,” Homological Mirror Symmetry: New Developments and Perspectives (A. Kapustin M. Kreuser, K-G. Schlesinger, eds) Springer, New York, USA, 2009 |
| [10] | F. Bulnes, “Geometrical Langlands Ramifications and Differential Operators Classification by Coherent D-Modules in Field Theory,” Journal of Mathematics and System Science, Vol. 3, no. 10, 2013, USA, pp491-507. |
| [11] | C. Teleman, The quantization conjecture revised, Ann. Of Math. (2) 152 (2000), 1-43. |
| [12] | B.Toën,The homotopy theory of dg-categories and derived Morita theory, Invent. Math. 167 (2007), no. 3, 615-667. |
| [13] | B.Toën, M. Vaquié, Moduli of objects in dg-categories, Ann. Sci. cole Norm. Sup. (4) 40 (2007), no. 3, 387-444. |
| [14] | E. Frenkel, C. Teleman, Geometric Langlands Correspondence Near Opers, Available at arXiv:1306.0876v1. |
APA Style
Yuri Stropovsvky. (2014). Functors on ∞- Categories and the Yoneda Embedding. Pure and Applied Mathematics Journal, 3(6-2), 20-25. https://doi.org/10.11648/j.pamj.s.2014030602.14
ACS Style
Yuri Stropovsvky. Functors on ∞- Categories and the Yoneda Embedding. Pure Appl. Math. J. 2014, 3(6-2), 20-25. doi: 10.11648/j.pamj.s.2014030602.14
AMA Style
Yuri Stropovsvky. Functors on ∞- Categories and the Yoneda Embedding. Pure Appl Math J. 2014;3(6-2):20-25. doi: 10.11648/j.pamj.s.2014030602.14
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.pamj.s.2014030602.14,
author = {Yuri Stropovsvky},
title = {Functors on ∞- Categories and the Yoneda Embedding},
journal = {Pure and Applied Mathematics Journal},
volume = {3},
number = {6-2},
pages = {20-25},
doi = {10.11648/j.pamj.s.2014030602.14},
url = {https://doi.org/10.11648/j.pamj.s.2014030602.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2014030602.14},
abstract = {Through the application of the Yoneda embedding in the context of the ∞- categories is obtained a classification of functors with their corresponding extended functors in the geometrical Langlands program. Also is obtained a functor formula that can be considered in the extending of functors to obtaining of generalized Verma modules. In this isomorphism formula are considered the Verma modules as classifying spaces of these functors.},
year = {2014}
}
TY - JOUR T1 - Functors on ∞- Categories and the Yoneda Embedding AU - Yuri Stropovsvky Y1 - 2014/11/24 PY - 2014 N1 - https://doi.org/10.11648/j.pamj.s.2014030602.14 DO - 10.11648/j.pamj.s.2014030602.14 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 20 EP - 25 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.s.2014030602.14 AB - Through the application of the Yoneda embedding in the context of the ∞- categories is obtained a classification of functors with their corresponding extended functors in the geometrical Langlands program. Also is obtained a functor formula that can be considered in the extending of functors to obtaining of generalized Verma modules. In this isomorphism formula are considered the Verma modules as classifying spaces of these functors. VL - 3 IS - 6-2 ER -
Email: