Colimits of internal categories
Abstract
We show that for an extensive $1$-category $\mathcal{E}$ with pullback-stable coequalisers admitting free internal categories over internal graphs, the $2$-category $\mathbf{Cat}(\mathcal{E})$ of internal categories, functors and natural transformations has finite $2$-colimits. In addition, $\mathbf{Cat}(\mathcal{E})$ is extensive and codescent coequalisers are stable under pullback along discrete Conduché fibrations. Moreover, we give converse results to this.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Algebraic structures and combinatorial models
Geometric and Algebraic Topology
Publication details
- Journal / source
- Bulletin of the Belgian Mathematical Society - Simon Stevin
- Volume
- 33
- Issue
- 3
- Publication date
- 20 July 2026
- Language
- EN