Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

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


a1 Dept. Matemàtica Aplicada II, Universitat Politècnica de Catalunya, 08071 Barcelona, Spain. e-mail:


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.

(Received January 17 2005)

(Revised January 25 2006)