English

Quantaloidal Completions of Order-enriched Categories and Their Applications

Category Theory 2023-06-22 v2

Abstract

By introducing the concept of quantaloidal completions for an order-enriched category, relationships between the category of quantaloids and the category of order-enriched categories are studied. It is proved that quantaloidal completions for an order-enriched category can be fully characterized as compatible quotients of the power-set completion. As applications, we show that a special type of injective hull of an order-enriched category is the MacNeille completion; the free quantaloid over an order-enriched category is the Down-set completion.

Keywords

Cite

@article{arxiv.2211.10932,
  title  = {Quantaloidal Completions of Order-enriched Categories and Their Applications},
  author = {Min Liu and Yulin Li},
  journal= {arXiv preprint arXiv:2211.10932},
  year   = {2023}
}