Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-29T18:53:34.606Z Has data issue: false hasContentIssue false
  • English
  • Français

A strict totally coordinatized version of Kapranov and Voevodsky's 2-category 2Vect

Published online by Cambridge University Press:  01 May 2007

JOSEP ELGUETA
JOSEP ELGUETA*
Affiliation:
Dept. Matemàtica Aplicada II, Universitat Politècnica de Catalunya, 08071 Barcelona, Spain. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we describe the 2-category 2Mat of 2-matrices, i.e., a strict totally coordinatized version of the 2-category 2Vect of Kapranov and Voevodsky finite dimensional 2-vector spaces, analogous to the category Mat of matrices which appears as the coordinatized version of the category Vect of finite dimensional vector spaces. In particular, explicit formulas for the composition of 1-morphisms and the two compositions between 2-morphisms are given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 3 , May 2007 , pp. 407 - 428
Copyright
Copyright © Cambridge Philosophical Society 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Baez, J. and Lauda, A.. Higher-dimensional algebra v: 2-groups. Theory Appl. Cat. 12 (2004), 423–491.Google Scholar
[2]Elgueta, J.. Representation theory of 2-groups on Kapranov and Voevodsky's 2-vector spaces. Arxiv: math. CT/0408120 (2004), to appear in Adv. Math.Google Scholar
[3]Kapranov, M. and Voevodsky, V.. 2-categories and Zamolodchikov tetrahedra equations. In Proc. Sympos. Pure Math. vol. 56 (2) (1994), 177–260.Google Scholar
[4]Neuchl, M.. Representation theory of Hopf categories. PhD Dissertation (University of Munich, 1997).Google Scholar
[5]Power, J., Gordon, R. and Street, R.. Coherence for tricategories. In Memoirs of the AMS, vol. 117, (1995).Google Scholar
[6]Yetter, D.. Categorical linear algebra. A setting for questions from physics and low-dimensional topology. Kansas State University preprint.Google Scholar