A strict totally coordinatized version of Kapranov and Voevodsky's 2-category 2Vect
Josep Elgueta · Mathematical Proceedings of the Cambridge Philosophical Society · 2007
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.