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The Exact Completion for Regular Categories enriched in Posets
- Publication Year :
- 2021
- Publisher :
- arXiv, 2021.
-
Abstract
- We construct an exact completion for regular categories enriched in the cartesian closed category $\mathsf{Pos}$ of partially ordered sets and monotone functions by employing a suitable calculus of relations. We then characterize the embedding of any regular category into its completion and use this to obtain examples of concrete categories which arise as such completions. In particular, we prove that the exact completion in this enriched sense of both the categories of Stone and Priestley spaces is the category of compact ordered spaces of L. Nachbin. Finally, we consider the relationship between the enriched exact completion and categories of internal posets in ordinary categories.<br />Comment: 42 pages. To appear in Journal of Pure and Applied Algebra
- Subjects :
- Algebra and Number Theory
18E08, 06F05, 18D20
Mathematics::General Topology
Mathematics - Category Theory
Construct (python library)
Algebra
Cartesian closed category
Monotone polygon
Mathematics::Category Theory
FOS: Mathematics
Embedding
Regular category
Category Theory (math.CT)
Partially ordered set
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....573d49466163c24d73c135e2fed2afb3
- Full Text :
- https://doi.org/10.48550/arxiv.2101.10989