A strict totally coordinatized version of Kapranov and Voevodsky's 2-category {\bf 2Vect}

TL;DR

This paper provides a detailed, explicit construction of a strict, totally coordinatized 2-category of finite-dimensional 2-vector spaces, including formulas for morphism compositions, enhancing the understanding of 2-categorical structures.

Contribution

It introduces a concrete, strict version of Kapranov and Voevodsky's 2-category with explicit composition formulas, advancing the explicit algebraic understanding of 2-vector spaces.

Findings

Explicit formulas for composition of 1-morphisms

Concrete description of the strict 2-category structure

Enhanced clarity on 2-morphism compositions

Abstract

We give a concrete description of a strict totally coordinatized version of Kapranov and Voevodsky's 2-category of finite dimensional 2-vector spaces. In particular, we give explicit formulas for composition of 1-morphisms and the two compositions between 2-morphisms