Comparison of the colimit and the 2-colimit

Abstract

The 2-colimit (also referred to as a pseudo colimit) is the 2-categorical analogue of the colimit and as such, a very important construction. Calculating it is, however, more involved than calculating the colimit. The aim of this paper is to give a condition under which these two constructions coincide. Tough the setting under which our results are applicable is very specific, it is, in fact, fairly important: As shown in a previous paper, the fundamental groupoid can be calculated using the 2-colimit. The results of this paper corresponds precisely to the situation of calculating the fundamental groupoid from a finite covering. We also optimise our condition in the last section, reducing from exponential complexity to a polynomial one.