Comparison of the colimit and the 2-colimit
- 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.
| Author: | Ilia Pirashvili |
|---|---|
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/108687 |
| ISSN: | 2193-8407OPAC |
| ISSN: | 1512-2891OPAC |
| Parent Title (English): | Journal of Homotopy and Related Structures |
| Publisher: | Springer Science and Business Media LLC |
| Type: | Article |
| Language: | English |
| Date of first Publication: | 2023/10/04 |
| Release Date: | 2023/10/26 |
| Tag: | Geometry and Topology; Algebra and Number Theory |
| Volume: | 18 |
| First Page: | 397 |
| Last Page: | 420 |
| DOI: | https://doi.org/10.1007/s40062-023-00331-4 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Algebra und Zahlentheorie | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
