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arXiv · 2211.10932

Quantaloidal Completions of Order-enriched Categories and Their Applications

Min Liu·Yulin Li
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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.

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BibTeXRIS

Min Liu, Yulin Li. 2022-11-20. Quantaloidal Completions of Order-enriched Categories and Their Applications. https://doi.org/10.46298/entics.10339

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