TY  - JOUR
A1  - Pirashvili, Ilia
T1  - Comparison of the colimit and the 2-colimit
T2  - Journal of Homotopy and Related Structures
N2  - 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.
KW  - Geometry and Topology
KW  - Algebra and Number Theory
Y1  - 2023
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/108687
SN  - 2193-8407
SN  - 1512-2891
VL  - 18
SP  - 397
EP  - 420
PB  - Springer Science and Business Media LLC
ER  -