The 2-group of symmetries of a split chain complex

Report, Article, Preprint English OPEN
Elgueta, Josep;
  • Publisher: Elsevier BV
  • Journal: Journal of Algebra,volume 351,issue 1,pages319-349 (issn: 0021-8693)
  • Publisher copyright policies & self-archiving
  • Related identifiers: doi: 10.1016/j.jalgebra.2011.11.016
  • Subject: Mathematics - Category Theory | :Matemàtiques i estadística::Àlgebra::Teoria K [Àrees temàtiques de la UPC] | K-teoria | Homologia | K-theory | Algebra and Number Theory | Homology theory | :19 K-theory [Classificació AMS] | Mathematics - K-Theory and Homology
    arxiv: Mathematics::Category Theory

We explicitly compute the 2-group of self-equivalences and (homotopy classes of) chain homotopies between them for any {\it split} chain complex $A_{\bullet}$ in an arbitrary $\kb$-linear abelian category ($\kb$ any commutative ring with unit). In particular, it is show... View more
  • References (15)
    15 references, page 1 of 2

    [1] J. Baez and A. Crans. Higher-dimensional algebra VI: Lie 2-algebras. Theory Appl. Categ., 12:492-538, 2004 (also available as arXiv: math.QA/0307263).

    [2] J. Baez and A. Lauda. Higher-dimensional algebra V: 2-groups. Theory Appl. Categ., 12:423-491, 2004 (also available as arXiv: math.QA/0307200).

    [3] J. Benabou. Introduction to bicategories. In Reports of the Midwest Category Seminar (LNM, volume 47), pages 1-77. Springer, 1967.

    [4] J. Elgueta. Representation theory of 2-groups on Kapranov and Voevodsky 2-vector spaces. Adv. Math., 213:53-92, 2007 (previous version available as math.CT/0408120).

    [5] J. Elgueta. Generalized 2-vector spaces and general linear 2-groups. J. Pure Appl. Alg., 212:2067- 2091, 2008.

    [6] J. Elgueta. On the regular representation of an (essentially) finite 2-group. arXiv:0907.0978, 2009.

    [7] P. Gabriel and M. Zisman. Calculus of fractions and homotopy theory. Springer Verlag, 1967.

    [8] A. Garzon and H. Inassaridze. Semidirect product of categorical groups, obstruction theory. Hom., Hom. and Applications, 3:111-138, 2001.

    [9] M. Kapranov and V. Voevodsky. 2-categories and Zamolodchikov tetrahedra equations. In Proc. Sympos. Pure Math., volume 56(2), pages 177-260. American Mathematical Society, 1994.

    [10] G.M. Kelly and R. Street. Review of the elements of 2-categories. In Proceedings of the Category Seminar, Sydney (LNM, volume 420), pages 75-103. Springer, 1974.

  • Related Organizations (3)
  • Metrics